Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [322,2,Mod(93,322)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(322, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("322.93");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.57118294509\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.1767277521.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 93.4 | ||
Root | \(-1.54162 + 1.88572i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 322.93 |
Dual form | 322.2.e.b.277.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).
\(n\) | \(185\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 1.60400 | + | 2.77821i | 0.926069 | + | 1.60400i | 0.789833 | + | 0.613321i | \(0.210167\pi\) |
0.136235 | + | 0.990677i | \(0.456500\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.79990 | − | 3.11751i | 0.804938 | − | 1.39419i | −0.111396 | − | 0.993776i | \(-0.535532\pi\) |
0.916333 | − | 0.400417i | \(-0.131135\pi\) | |||||||
\(6\) | −3.20800 | −1.30966 | ||||||||
\(7\) | 1.82854 | − | 1.91218i | 0.691124 | − | 0.722736i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −3.64562 | + | 6.31440i | −1.21521 | + | 2.10480i | ||||
\(10\) | 1.79990 | + | 3.11751i | 0.569177 | + | 0.985843i | ||||
\(11\) | 2.04162 | + | 3.53619i | 0.615572 | + | 1.06620i | 0.990284 | + | 0.139061i | \(0.0444083\pi\) |
−0.374712 | + | 0.927141i | \(0.622258\pi\) | |||||||
\(12\) | 1.60400 | − | 2.77821i | 0.463034 | − | 0.801999i | ||||
\(13\) | 0.932540 | 0.258640 | 0.129320 | − | 0.991603i | \(-0.458721\pi\) | ||||
0.129320 | + | 0.991603i | \(0.458721\pi\) | |||||||
\(14\) | 0.741726 | + | 2.53965i | 0.198235 | + | 0.678751i | ||||
\(15\) | 11.5481 | 2.98171 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.17514 | − | 5.49951i | −0.770085 | − | 1.33383i | −0.937516 | − | 0.347942i | \(-0.886881\pi\) |
0.167431 | − | 0.985884i | \(-0.446453\pi\) | |||||||
\(18\) | −3.64562 | − | 6.31440i | −0.859281 | − | 1.48832i | ||||
\(19\) | −2.00789 | + | 3.47777i | −0.460642 | + | 0.797855i | −0.998993 | − | 0.0448656i | \(-0.985714\pi\) |
0.538351 | + | 0.842721i | \(0.319047\pi\) | |||||||
\(20\) | −3.59979 | −0.804938 | ||||||||
\(21\) | 8.24541 | + | 2.01293i | 1.79930 | + | 0.439258i | ||||
\(22\) | −4.08324 | −0.870550 | ||||||||
\(23\) | −0.500000 | + | 0.866025i | −0.104257 | + | 0.180579i | ||||
\(24\) | 1.60400 | + | 2.77821i | 0.327415 | + | 0.567099i | ||||
\(25\) | −3.97924 | − | 6.89225i | −0.795849 | − | 1.37845i | ||||
\(26\) | −0.466270 | + | 0.807603i | −0.0914431 | + | 0.158384i | ||||
\(27\) | −13.7663 | −2.64932 | ||||||||
\(28\) | −2.57027 | − | 0.627473i | −0.485735 | − | 0.118581i | ||||
\(29\) | −5.14054 | −0.954574 | −0.477287 | − | 0.878748i | \(-0.658380\pi\) | ||||
−0.477287 | + | 0.878748i | \(0.658380\pi\) | |||||||
\(30\) | −5.77406 | + | 10.0010i | −1.05419 | + | 1.82592i | ||||
\(31\) | −0.766165 | − | 1.32704i | −0.137607 | − | 0.238343i | 0.788983 | − | 0.614415i | \(-0.210608\pi\) |
−0.926590 | + | 0.376072i | \(0.877275\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −6.54951 | + | 11.3441i | −1.14012 | + | 1.97475i | ||||
\(34\) | 6.35028 | 1.08906 | ||||||||
\(35\) | −2.67006 | − | 9.14222i | −0.451322 | − | 1.54532i | ||||
\(36\) | 7.29124 | 1.21521 | ||||||||
\(37\) | −0.528647 | + | 0.915643i | −0.0869090 | + | 0.150531i | −0.906203 | − | 0.422843i | \(-0.861032\pi\) |
0.819294 | + | 0.573374i | \(0.194366\pi\) | |||||||
\(38\) | −2.00789 | − | 3.47777i | −0.325723 | − | 0.564169i | ||||
\(39\) | 1.49579 | + | 2.59079i | 0.239518 | + | 0.414858i | ||||
\(40\) | 1.79990 | − | 3.11751i | 0.284588 | − | 0.492922i | ||||
\(41\) | −2.51655 | −0.393019 | −0.196509 | − | 0.980502i | \(-0.562961\pi\) | ||||
−0.196509 | + | 0.980502i | \(0.562961\pi\) | |||||||
\(42\) | −5.86595 | + | 6.13427i | −0.905137 | + | 0.946538i | ||||
\(43\) | 0.532330 | 0.0811795 | 0.0405898 | − | 0.999176i | \(-0.487076\pi\) | ||||
0.0405898 | + | 0.999176i | \(0.487076\pi\) | |||||||
\(44\) | 2.04162 | − | 3.53619i | 0.307786 | − | 0.533101i | ||||
\(45\) | 13.1235 | + | 22.7305i | 1.95633 | + | 3.38846i | ||||
\(46\) | −0.500000 | − | 0.866025i | −0.0737210 | − | 0.127688i | ||||
\(47\) | 3.63352 | − | 6.29344i | 0.530003 | − | 0.917993i | −0.469384 | − | 0.882994i | \(-0.655524\pi\) |
0.999387 | − | 0.0349986i | \(-0.0111427\pi\) | |||||||
\(48\) | −3.20800 | −0.463034 | ||||||||
\(49\) | −0.312869 | − | 6.99300i | −0.0446956 | − | 0.999001i | ||||
\(50\) | 7.95849 | 1.12550 | ||||||||
\(51\) | 10.1858 | − | 17.6424i | 1.42630 | − | 2.47043i | ||||
\(52\) | −0.466270 | − | 0.807603i | −0.0646600 | − | 0.111994i | ||||
\(53\) | −0.212204 | − | 0.367548i | −0.0291484 | − | 0.0504866i | 0.851083 | − | 0.525031i | \(-0.175946\pi\) |
−0.880232 | + | 0.474544i | \(0.842613\pi\) | |||||||
\(54\) | 6.88314 | − | 11.9219i | 0.936676 | − | 1.62237i | ||||
\(55\) | 14.6988 | 1.98199 | ||||||||
\(56\) | 1.82854 | − | 1.91218i | 0.244349 | − | 0.255526i | ||||
\(57\) | −12.8826 | −1.70634 | ||||||||
\(58\) | 2.57027 | − | 4.45183i | 0.337493 | − | 0.584555i | ||||
\(59\) | 0.384537 | + | 0.666038i | 0.0500625 | + | 0.0867108i | 0.889971 | − | 0.456018i | \(-0.150725\pi\) |
−0.839908 | + | 0.542728i | \(0.817391\pi\) | |||||||
\(60\) | −5.77406 | − | 10.0010i | −0.745427 | − | 1.29112i | ||||
\(61\) | −5.86659 | + | 10.1612i | −0.751140 | + | 1.30101i | 0.196131 | + | 0.980578i | \(0.437162\pi\) |
−0.947271 | + | 0.320435i | \(0.896171\pi\) | |||||||
\(62\) | 1.53233 | 0.194606 | ||||||||
\(63\) | 5.40810 | + | 18.5172i | 0.681357 | + | 2.33295i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.67847 | − | 2.90720i | 0.208189 | − | 0.360594i | ||||
\(66\) | −6.54951 | − | 11.3441i | −0.806189 | − | 1.39636i | ||||
\(67\) | 2.37945 | + | 4.12134i | 0.290697 | + | 0.503501i | 0.973975 | − | 0.226657i | \(-0.0727796\pi\) |
−0.683278 | + | 0.730158i | \(0.739446\pi\) | |||||||
\(68\) | −3.17514 | + | 5.49951i | −0.385042 | + | 0.666913i | ||||
\(69\) | −3.20800 | −0.386197 | ||||||||
\(70\) | 9.25242 | + | 2.25877i | 1.10588 | + | 0.269975i | ||||
\(71\) | −5.83072 | −0.691979 | −0.345989 | − | 0.938238i | \(-0.612457\pi\) | ||||
−0.345989 | + | 0.938238i | \(0.612457\pi\) | |||||||
\(72\) | −3.64562 | + | 6.31440i | −0.429640 | + | 0.744159i | ||||
\(73\) | 5.69870 | + | 9.87045i | 0.666983 | + | 1.15525i | 0.978744 | + | 0.205088i | \(0.0657480\pi\) |
−0.311761 | + | 0.950161i | \(0.600919\pi\) | |||||||
\(74\) | −0.528647 | − | 0.915643i | −0.0614540 | − | 0.106441i | ||||
\(75\) | 12.7654 | − | 22.1103i | 1.47402 | − | 2.55308i | ||||
\(76\) | 4.01578 | 0.460642 | ||||||||
\(77\) | 10.4950 | + | 2.56213i | 1.19602 | + | 0.291981i | ||||
\(78\) | −2.99158 | −0.338730 | ||||||||
\(79\) | 1.78335 | − | 3.08885i | 0.200642 | − | 0.347523i | −0.748093 | − | 0.663594i | \(-0.769030\pi\) |
0.948736 | + | 0.316071i | \(0.102364\pi\) | |||||||
\(80\) | 1.79990 | + | 3.11751i | 0.201234 | + | 0.348548i | ||||
\(81\) | −11.1442 | − | 19.3024i | −1.23825 | − | 2.14471i | ||||
\(82\) | 1.25827 | − | 2.17939i | 0.138953 | − | 0.240674i | ||||
\(83\) | −12.4547 | −1.36708 | −0.683541 | − | 0.729912i | \(-0.739561\pi\) | ||||
−0.683541 | + | 0.729912i | \(0.739561\pi\) | |||||||
\(84\) | −2.37945 | − | 8.14720i | −0.259620 | − | 0.888932i | ||||
\(85\) | −22.8597 | −2.47948 | ||||||||
\(86\) | −0.266165 | + | 0.461011i | −0.0287013 | + | 0.0497121i | ||||
\(87\) | −8.24541 | − | 14.2815i | −0.884001 | − | 1.53113i | ||||
\(88\) | 2.04162 | + | 3.53619i | 0.217638 | + | 0.376959i | ||||
\(89\) | 5.49134 | − | 9.51129i | 0.582081 | − | 1.00819i | −0.413151 | − | 0.910662i | \(-0.635572\pi\) |
0.995232 | − | 0.0975318i | \(-0.0310948\pi\) | |||||||
\(90\) | −26.2469 | −2.76667 | ||||||||
\(91\) | 1.70519 | − | 1.78318i | 0.178752 | − | 0.186929i | ||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 2.45785 | − | 4.25713i | 0.254868 | − | 0.441444i | ||||
\(94\) | 3.63352 | + | 6.29344i | 0.374769 | + | 0.649119i | ||||
\(95\) | 7.22799 | + | 12.5192i | 0.741576 | + | 1.28445i | ||||
\(96\) | 1.60400 | − | 2.77821i | 0.163707 | − | 0.283549i | ||||
\(97\) | 16.4419 | 1.66943 | 0.834713 | − | 0.550685i | \(-0.185633\pi\) | ||||
0.834713 | + | 0.550685i | \(0.185633\pi\) | |||||||
\(98\) | 6.21255 | + | 3.22555i | 0.627563 | + | 0.325830i | ||||
\(99\) | −29.7719 | −2.99219 | ||||||||
\(100\) | −3.97924 | + | 6.89225i | −0.397924 | + | 0.689225i | ||||
\(101\) | −8.55232 | − | 14.8131i | −0.850988 | − | 1.47395i | −0.880318 | − | 0.474384i | \(-0.842671\pi\) |
0.0293304 | − | 0.999570i | \(-0.490663\pi\) | |||||||
\(102\) | 10.1858 | + | 17.6424i | 1.00855 | + | 1.74686i | ||||
\(103\) | 6.74962 | − | 11.6907i | 0.665060 | − | 1.15192i | −0.314210 | − | 0.949354i | \(-0.601739\pi\) |
0.979269 | − | 0.202563i | \(-0.0649272\pi\) | |||||||
\(104\) | 0.932540 | 0.0914431 | ||||||||
\(105\) | 21.1162 | − | 22.0821i | 2.06073 | − | 2.15499i | ||||
\(106\) | 0.424408 | 0.0412221 | ||||||||
\(107\) | −3.51297 | + | 6.08465i | −0.339612 | + | 0.588225i | −0.984360 | − | 0.176170i | \(-0.943629\pi\) |
0.644748 | + | 0.764395i | \(0.276962\pi\) | |||||||
\(108\) | 6.88314 | + | 11.9219i | 0.662330 | + | 1.14719i | ||||
\(109\) | 6.36508 | + | 11.0246i | 0.609664 | + | 1.05597i | 0.991296 | + | 0.131655i | \(0.0420290\pi\) |
−0.381632 | + | 0.924315i | \(0.624638\pi\) | |||||||
\(110\) | −7.34941 | + | 12.7295i | −0.700738 | + | 1.21371i | ||||
\(111\) | −3.39179 | −0.321935 | ||||||||
\(112\) | 0.741726 | + | 2.53965i | 0.0700865 | + | 0.239975i | ||||
\(113\) | −6.27371 | −0.590181 | −0.295090 | − | 0.955469i | \(-0.595350\pi\) | ||||
−0.295090 | + | 0.955469i | \(0.595350\pi\) | |||||||
\(114\) | 6.44131 | − | 11.1567i | 0.603284 | − | 1.04492i | ||||
\(115\) | 1.79990 | + | 3.11751i | 0.167841 | + | 0.290709i | ||||
\(116\) | 2.57027 | + | 4.45183i | 0.238643 | + | 0.413342i | ||||
\(117\) | −3.39969 | + | 5.88843i | −0.314301 | + | 0.544385i | ||||
\(118\) | −0.769075 | −0.0707990 | ||||||||
\(119\) | −16.3219 | − | 3.98463i | −1.49623 | − | 0.365271i | ||||
\(120\) | 11.5481 | 1.05419 | ||||||||
\(121\) | −2.83643 | + | 4.91285i | −0.257858 | + | 0.446622i | ||||
\(122\) | −5.86659 | − | 10.1612i | −0.531136 | − | 0.919955i | ||||
\(123\) | −4.03654 | − | 6.99149i | −0.363962 | − | 0.630401i | ||||
\(124\) | −0.766165 | + | 1.32704i | −0.0688036 | + | 0.119171i | ||||
\(125\) | −10.6499 | −0.952559 | ||||||||
\(126\) | −18.7404 | − | 4.57506i | −1.66953 | − | 0.407579i | ||||
\(127\) | 6.97602 | 0.619022 | 0.309511 | − | 0.950896i | \(-0.399835\pi\) | ||||
0.309511 | + | 0.950896i | \(0.399835\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0.853856 | + | 1.47892i | 0.0751778 | + | 0.130212i | ||||
\(130\) | 1.67847 | + | 2.90720i | 0.147212 | + | 0.254978i | ||||
\(131\) | 4.21220 | − | 7.29575i | 0.368022 | − | 0.637433i | −0.621234 | − | 0.783625i | \(-0.713368\pi\) |
0.989256 | + | 0.146192i | \(0.0467018\pi\) | |||||||
\(132\) | 13.0990 | 1.14012 | ||||||||
\(133\) | 2.97861 | + | 10.1987i | 0.258278 | + | 0.884339i | ||||
\(134\) | −4.75891 | −0.411107 | ||||||||
\(135\) | −24.7778 | + | 42.9165i | −2.13254 | + | 3.69366i | ||||
\(136\) | −3.17514 | − | 5.49951i | −0.272266 | − | 0.471579i | ||||
\(137\) | −5.39611 | − | 9.34634i | −0.461021 | − | 0.798512i | 0.537991 | − | 0.842950i | \(-0.319183\pi\) |
−0.999012 | + | 0.0444388i | \(0.985850\pi\) | |||||||
\(138\) | 1.60400 | − | 2.77821i | 0.136541 | − | 0.236497i | ||||
\(139\) | −7.85793 | −0.666501 | −0.333251 | − | 0.942838i | \(-0.608145\pi\) | ||||
−0.333251 | + | 0.942838i | \(0.608145\pi\) | |||||||
\(140\) | −6.58237 | + | 6.88345i | −0.556312 | + | 0.581758i | ||||
\(141\) | 23.3126 | 1.96328 | ||||||||
\(142\) | 2.91536 | − | 5.04955i | 0.244651 | − | 0.423749i | ||||
\(143\) | 1.90389 | + | 3.29764i | 0.159212 | + | 0.275762i | ||||
\(144\) | −3.64562 | − | 6.31440i | −0.303802 | − | 0.526200i | ||||
\(145\) | −9.25242 | + | 16.0257i | −0.768372 | + | 1.33086i | ||||
\(146\) | −11.3974 | −0.943256 | ||||||||
\(147\) | 18.9262 | − | 12.0860i | 1.56100 | − | 0.996835i | ||||
\(148\) | 1.05729 | 0.0869090 | ||||||||
\(149\) | 5.23394 | − | 9.06546i | 0.428781 | − | 0.742671i | −0.567984 | − | 0.823040i | \(-0.692276\pi\) |
0.996765 | + | 0.0803685i | \(0.0256097\pi\) | |||||||
\(150\) | 12.7654 | + | 22.1103i | 1.04229 | + | 1.80530i | ||||
\(151\) | −2.61634 | − | 4.53163i | −0.212915 | − | 0.368779i | 0.739711 | − | 0.672925i | \(-0.234962\pi\) |
−0.952625 | + | 0.304146i | \(0.901629\pi\) | |||||||
\(152\) | −2.00789 | + | 3.47777i | −0.162861 | + | 0.282084i | ||||
\(153\) | 46.3014 | 3.74325 | ||||||||
\(154\) | −7.46638 | + | 7.80790i | −0.601658 | + | 0.629178i | ||||
\(155\) | −5.51607 | −0.443061 | ||||||||
\(156\) | 1.49579 | − | 2.59079i | 0.119759 | − | 0.207429i | ||||
\(157\) | 9.84432 | + | 17.0509i | 0.785663 | + | 1.36081i | 0.928602 | + | 0.371076i | \(0.121011\pi\) |
−0.142940 | + | 0.989731i | \(0.545656\pi\) | |||||||
\(158\) | 1.78335 | + | 3.08885i | 0.141875 | + | 0.245736i | ||||
\(159\) | 0.680749 | − | 1.17909i | 0.0539869 | − | 0.0935081i | ||||
\(160\) | −3.59979 | −0.284588 | ||||||||
\(161\) | 0.741726 | + | 2.53965i | 0.0584562 | + | 0.200153i | ||||
\(162\) | 22.2884 | 1.75115 | ||||||||
\(163\) | −7.48650 | + | 12.9670i | −0.586388 | + | 1.01565i | 0.408313 | + | 0.912842i | \(0.366117\pi\) |
−0.994701 | + | 0.102812i | \(0.967216\pi\) | |||||||
\(164\) | 1.25827 | + | 2.17939i | 0.0982547 | + | 0.170182i | ||||
\(165\) | 23.5769 | + | 40.8363i | 1.83546 | + | 3.17910i | ||||
\(166\) | 6.22735 | − | 10.7861i | 0.483336 | − | 0.837163i | ||||
\(167\) | 5.08149 | 0.393218 | 0.196609 | − | 0.980482i | \(-0.437007\pi\) | ||||
0.196609 | + | 0.980482i | \(0.437007\pi\) | |||||||
\(168\) | 8.24541 | + | 2.01293i | 0.636147 | + | 0.155301i | ||||
\(169\) | −12.1304 | −0.933105 | ||||||||
\(170\) | 11.4298 | − | 19.7971i | 0.876629 | − | 1.51837i | ||||
\(171\) | −14.6400 | − | 25.3572i | −1.11955 | − | 1.93912i | ||||
\(172\) | −0.266165 | − | 0.461011i | −0.0202949 | − | 0.0351518i | ||||
\(173\) | 6.01245 | − | 10.4139i | 0.457118 | − | 0.791752i | −0.541689 | − | 0.840579i | \(-0.682215\pi\) |
0.998807 | + | 0.0488272i | \(0.0155484\pi\) | |||||||
\(174\) | 16.4908 | 1.25017 | ||||||||
\(175\) | −20.4554 | − | 4.99374i | −1.54629 | − | 0.377491i | ||||
\(176\) | −4.08324 | −0.307786 | ||||||||
\(177\) | −1.23359 | + | 2.13665i | −0.0927226 | + | 0.160600i | ||||
\(178\) | 5.49134 | + | 9.51129i | 0.411594 | + | 0.712901i | ||||
\(179\) | 3.99492 | + | 6.91940i | 0.298594 | + | 0.517180i | 0.975815 | − | 0.218600i | \(-0.0701490\pi\) |
−0.677220 | + | 0.735780i | \(0.736816\pi\) | |||||||
\(180\) | 13.1235 | − | 22.7305i | 0.978165 | − | 1.69423i | ||||
\(181\) | 0.525446 | 0.0390561 | 0.0195280 | − | 0.999809i | \(-0.493784\pi\) | ||||
0.0195280 | + | 0.999809i | \(0.493784\pi\) | |||||||
\(182\) | 0.691689 | + | 2.36833i | 0.0512714 | + | 0.175552i | ||||
\(183\) | −37.6400 | −2.78243 | ||||||||
\(184\) | −0.500000 | + | 0.866025i | −0.0368605 | + | 0.0638442i | ||||
\(185\) | 1.90302 | + | 3.29612i | 0.139913 | + | 0.242336i | ||||
\(186\) | 2.45785 | + | 4.25713i | 0.180219 | + | 0.312148i | ||||
\(187\) | 12.9649 | − | 22.4558i | 0.948085 | − | 1.64213i | ||||
\(188\) | −7.26704 | −0.530003 | ||||||||
\(189\) | −25.1722 | + | 26.3236i | −1.83101 | + | 1.91476i | ||||
\(190\) | −14.4560 | −1.04875 | ||||||||
\(191\) | 2.46778 | − | 4.27432i | 0.178562 | − | 0.309279i | −0.762826 | − | 0.646604i | \(-0.776189\pi\) |
0.941388 | + | 0.337325i | \(0.109522\pi\) | |||||||
\(192\) | 1.60400 | + | 2.77821i | 0.115759 | + | 0.200500i | ||||
\(193\) | 4.36238 | + | 7.55587i | 0.314011 | + | 0.543883i | 0.979227 | − | 0.202768i | \(-0.0649938\pi\) |
−0.665216 | + | 0.746651i | \(0.731660\pi\) | |||||||
\(194\) | −8.22097 | + | 14.2391i | −0.590231 | + | 1.02231i | ||||
\(195\) | 10.7691 | 0.771189 | ||||||||
\(196\) | −5.89969 | + | 3.76745i | −0.421406 | + | 0.269104i | ||||
\(197\) | −14.2413 | −1.01465 | −0.507326 | − | 0.861754i | \(-0.669366\pi\) | ||||
−0.507326 | + | 0.861754i | \(0.669366\pi\) | |||||||
\(198\) | 14.8859 | − | 25.7832i | 1.05790 | − | 1.83233i | ||||
\(199\) | 6.86000 | + | 11.8819i | 0.486292 | + | 0.842283i | 0.999876 | − | 0.0157567i | \(-0.00501571\pi\) |
−0.513584 | + | 0.858040i | \(0.671682\pi\) | |||||||
\(200\) | −3.97924 | − | 6.89225i | −0.281375 | − | 0.487356i | ||||
\(201\) | −7.63328 | + | 13.2212i | −0.538410 | + | 0.932553i | ||||
\(202\) | 17.1046 | 1.20348 | ||||||||
\(203\) | −9.39969 | + | 9.82963i | −0.659729 | + | 0.689905i | ||||
\(204\) | −20.3717 | −1.42630 | ||||||||
\(205\) | −4.52952 | + | 7.84536i | −0.316356 | + | 0.547944i | ||||
\(206\) | 6.74962 | + | 11.6907i | 0.470268 | + | 0.814528i | ||||
\(207\) | −3.64562 | − | 6.31440i | −0.253388 | − | 0.438881i | ||||
\(208\) | −0.466270 | + | 0.807603i | −0.0323300 | + | 0.0559972i | ||||
\(209\) | −16.3974 | −1.13423 | ||||||||
\(210\) | 8.56553 | + | 29.3282i | 0.591078 | + | 2.02384i | ||||
\(211\) | 1.96410 | 0.135214 | 0.0676072 | − | 0.997712i | \(-0.478464\pi\) | ||||
0.0676072 | + | 0.997712i | \(0.478464\pi\) | |||||||
\(212\) | −0.212204 | + | 0.367548i | −0.0145742 | + | 0.0252433i | ||||
\(213\) | −9.35246 | − | 16.1989i | −0.640820 | − | 1.10993i | ||||
\(214\) | −3.51297 | − | 6.08465i | −0.240142 | − | 0.415938i | ||||
\(215\) | 0.958138 | − | 1.65954i | 0.0653445 | − | 0.113180i | ||||
\(216\) | −13.7663 | −0.936676 | ||||||||
\(217\) | −3.93850 | − | 0.961496i | −0.267363 | − | 0.0652706i | ||||
\(218\) | −12.7302 | −0.862195 | ||||||||
\(219\) | −18.2814 | + | 31.6644i | −1.23534 | + | 2.13968i | ||||
\(220\) | −7.34941 | − | 12.7295i | −0.495497 | − | 0.858226i | ||||
\(221\) | −2.96095 | − | 5.12851i | −0.199175 | − | 0.344981i | ||||
\(222\) | 1.69590 | − | 2.93738i | 0.113821 | − | 0.197144i | ||||
\(223\) | 7.00667 | 0.469201 | 0.234601 | − | 0.972092i | \(-0.424622\pi\) | ||||
0.234601 | + | 0.972092i | \(0.424622\pi\) | |||||||
\(224\) | −2.57027 | − | 0.627473i | −0.171733 | − | 0.0419248i | ||||
\(225\) | 58.0272 | 3.86848 | ||||||||
\(226\) | 3.13685 | − | 5.43319i | 0.208660 | − | 0.361410i | ||||
\(227\) | 12.5699 | + | 21.7716i | 0.834290 | + | 1.44503i | 0.894607 | + | 0.446854i | \(0.147456\pi\) |
−0.0603165 | + | 0.998179i | \(0.519211\pi\) | |||||||
\(228\) | 6.44131 | + | 11.1567i | 0.426586 | + | 0.738868i | ||||
\(229\) | 7.92118 | − | 13.7199i | 0.523447 | − | 0.906636i | −0.476181 | − | 0.879347i | \(-0.657979\pi\) |
0.999628 | − | 0.0272888i | \(-0.00868737\pi\) | |||||||
\(230\) | −3.59979 | −0.237363 | ||||||||
\(231\) | 9.71589 | + | 33.2670i | 0.639258 | + | 2.18881i | ||||
\(232\) | −5.14054 | −0.337493 | ||||||||
\(233\) | −2.56249 | + | 4.43836i | −0.167874 | + | 0.290766i | −0.937672 | − | 0.347521i | \(-0.887024\pi\) |
0.769798 | + | 0.638287i | \(0.220357\pi\) | |||||||
\(234\) | −3.39969 | − | 5.88843i | −0.222244 | − | 0.384939i | ||||
\(235\) | −13.0799 | − | 22.6551i | −0.853239 | − | 1.47785i | ||||
\(236\) | 0.384537 | − | 0.666038i | 0.0250312 | − | 0.0433554i | ||||
\(237\) | 11.4419 | 0.743234 | ||||||||
\(238\) | 11.6118 | − | 12.1429i | 0.752678 | − | 0.787106i | ||||
\(239\) | −13.2069 | −0.854286 | −0.427143 | − | 0.904184i | \(-0.640480\pi\) | ||||
−0.427143 | + | 0.904184i | \(0.640480\pi\) | |||||||
\(240\) | −5.77406 | + | 10.0010i | −0.372714 | + | 0.645559i | ||||
\(241\) | −13.8311 | − | 23.9562i | −0.890940 | − | 1.54315i | −0.838750 | − | 0.544516i | \(-0.816713\pi\) |
−0.0521897 | − | 0.998637i | \(-0.516620\pi\) | |||||||
\(242\) | −2.83643 | − | 4.91285i | −0.182333 | − | 0.315810i | ||||
\(243\) | 15.1012 | − | 26.1560i | 0.968742 | − | 1.67791i | ||||
\(244\) | 11.7332 | 0.751140 | ||||||||
\(245\) | −22.3639 | − | 11.6113i | −1.42878 | − | 0.741819i | ||||
\(246\) | 8.07308 | 0.514721 | ||||||||
\(247\) | −1.87244 | + | 3.24316i | −0.119140 | + | 0.206357i | ||||
\(248\) | −0.766165 | − | 1.32704i | −0.0486515 | − | 0.0842669i | ||||
\(249\) | −19.9773 | − | 34.6017i | −1.26601 | − | 2.19280i | ||||
\(250\) | 5.32497 | − | 9.22312i | 0.336781 | − | 0.583321i | ||||
\(251\) | 13.8333 | 0.873147 | 0.436574 | − | 0.899669i | \(-0.356192\pi\) | ||||
0.436574 | + | 0.899669i | \(0.356192\pi\) | |||||||
\(252\) | 13.3323 | − | 13.9422i | 0.839858 | − | 0.878274i | ||||
\(253\) | −4.08324 | −0.256711 | ||||||||
\(254\) | −3.48801 | + | 6.04141i | −0.218857 | + | 0.379072i | ||||
\(255\) | −36.6669 | − | 63.5089i | −2.29617 | − | 3.97708i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −12.0746 | + | 20.9138i | −0.753192 | + | 1.30457i | 0.193076 | + | 0.981184i | \(0.438154\pi\) |
−0.946268 | + | 0.323383i | \(0.895180\pi\) | |||||||
\(258\) | −1.70771 | −0.106318 | ||||||||
\(259\) | 0.784222 | + | 2.68516i | 0.0487292 | + | 0.166848i | ||||
\(260\) | −3.35695 | −0.208189 | ||||||||
\(261\) | 18.7404 | − | 32.4594i | 1.16000 | − | 2.00919i | ||||
\(262\) | 4.21220 | + | 7.29575i | 0.260231 | + | 0.450733i | ||||
\(263\) | −14.1521 | − | 24.5122i | −0.872656 | − | 1.51149i | −0.859238 | − | 0.511575i | \(-0.829062\pi\) |
−0.0134181 | − | 0.999910i | \(-0.504271\pi\) | |||||||
\(264\) | −6.54951 | + | 11.3441i | −0.403095 | + | 0.698180i | ||||
\(265\) | −1.52778 | −0.0938507 | ||||||||
\(266\) | −10.3216 | − | 2.51980i | −0.632860 | − | 0.154499i | ||||
\(267\) | 35.2324 | 2.15619 | ||||||||
\(268\) | 2.37945 | − | 4.12134i | 0.145348 | − | 0.251751i | ||||
\(269\) | 15.1139 | + | 26.1781i | 0.921513 | + | 1.59611i | 0.797076 | + | 0.603879i | \(0.206379\pi\) |
0.124437 | + | 0.992228i | \(0.460288\pi\) | |||||||
\(270\) | −24.7778 | − | 42.9165i | −1.50793 | − | 2.61181i | ||||
\(271\) | 4.57665 | − | 7.92699i | 0.278012 | − | 0.481530i | −0.692879 | − | 0.721054i | \(-0.743658\pi\) |
0.970891 | + | 0.239524i | \(0.0769913\pi\) | |||||||
\(272\) | 6.35028 | 0.385042 | ||||||||
\(273\) | 7.68917 | + | 1.87714i | 0.465370 | + | 0.113610i | ||||
\(274\) | 10.7922 | 0.651982 | ||||||||
\(275\) | 16.2482 | − | 28.1427i | 0.979804 | − | 1.69707i | ||||
\(276\) | 1.60400 | + | 2.77821i | 0.0965493 | + | 0.167228i | ||||
\(277\) | −9.42722 | − | 16.3284i | −0.566426 | − | 0.981079i | −0.996915 | − | 0.0784836i | \(-0.974992\pi\) |
0.430489 | − | 0.902596i | \(-0.358341\pi\) | |||||||
\(278\) | 3.92897 | − | 6.80517i | 0.235644 | − | 0.408147i | ||||
\(279\) | 11.1726 | 0.668885 | ||||||||
\(280\) | −2.67006 | − | 9.14222i | −0.159566 | − | 0.546352i | ||||
\(281\) | 12.1176 | 0.722876 | 0.361438 | − | 0.932396i | \(-0.382286\pi\) | ||||
0.361438 | + | 0.932396i | \(0.382286\pi\) | |||||||
\(282\) | −11.6563 | + | 20.1893i | −0.694124 | + | 1.20226i | ||||
\(283\) | 6.60463 | + | 11.4396i | 0.392605 | + | 0.680011i | 0.992792 | − | 0.119848i | \(-0.0382408\pi\) |
−0.600188 | + | 0.799859i | \(0.704907\pi\) | |||||||
\(284\) | 2.91536 | + | 5.04955i | 0.172995 | + | 0.299636i | ||||
\(285\) | −23.1873 | + | 40.1617i | −1.37350 | + | 2.37897i | ||||
\(286\) | −3.80779 | −0.225159 | ||||||||
\(287\) | −4.60161 | + | 4.81209i | −0.271625 | + | 0.284049i | ||||
\(288\) | 7.29124 | 0.429640 | ||||||||
\(289\) | −11.6630 | + | 20.2010i | −0.686061 | + | 1.18829i | ||||
\(290\) | −9.25242 | − | 16.0257i | −0.543321 | − | 0.941060i | ||||
\(291\) | 26.3728 | + | 45.6791i | 1.54600 | + | 2.67776i | ||||
\(292\) | 5.69870 | − | 9.87045i | 0.333491 | − | 0.577624i | ||||
\(293\) | 14.8724 | 0.868858 | 0.434429 | − | 0.900706i | \(-0.356950\pi\) | ||||
0.434429 | + | 0.900706i | \(0.356950\pi\) | |||||||
\(294\) | 1.00368 | + | 22.4335i | 0.0585360 | + | 1.30835i | ||||
\(295\) | 2.76851 | 0.161189 | ||||||||
\(296\) | −0.528647 | + | 0.915643i | −0.0307270 | + | 0.0532207i | ||||
\(297\) | −28.1055 | − | 48.6802i | −1.63085 | − | 2.82471i | ||||
\(298\) | 5.23394 | + | 9.06546i | 0.303194 | + | 0.525148i | ||||
\(299\) | −0.466270 | + | 0.807603i | −0.0269651 | + | 0.0467049i | ||||
\(300\) | −25.5308 | −1.47402 | ||||||||
\(301\) | 0.973387 | − | 1.01791i | 0.0561051 | − | 0.0586714i | ||||
\(302\) | 5.23268 | 0.301107 | ||||||||
\(303\) | 27.4358 | − | 47.5202i | 1.57615 | − | 2.72996i | ||||
\(304\) | −2.00789 | − | 3.47777i | −0.115160 | − | 0.199464i | ||||
\(305\) | 21.1185 | + | 36.5783i | 1.20924 | + | 2.09447i | ||||
\(306\) | −23.1507 | + | 40.0982i | −1.32344 | + | 2.29226i | ||||
\(307\) | −10.6673 | −0.608812 | −0.304406 | − | 0.952542i | \(-0.598458\pi\) | ||||
−0.304406 | + | 0.952542i | \(0.598458\pi\) | |||||||
\(308\) | −3.02865 | − | 10.3700i | −0.172573 | − | 0.590887i | ||||
\(309\) | 43.3055 | 2.46356 | ||||||||
\(310\) | 2.75803 | − | 4.77705i | 0.156646 | − | 0.271318i | ||||
\(311\) | 8.45610 | + | 14.6464i | 0.479502 | + | 0.830521i | 0.999724 | − | 0.0235099i | \(-0.00748412\pi\) |
−0.520222 | + | 0.854031i | \(0.674151\pi\) | |||||||
\(312\) | 1.49579 | + | 2.59079i | 0.0846825 | + | 0.146674i | ||||
\(313\) | −13.2189 | + | 22.8959i | −0.747178 | + | 1.29415i | 0.201992 | + | 0.979387i | \(0.435259\pi\) |
−0.949170 | + | 0.314764i | \(0.898075\pi\) | |||||||
\(314\) | −19.6886 | −1.11109 | ||||||||
\(315\) | 67.4616 | + | 16.4692i | 3.80103 | + | 0.927937i | ||||
\(316\) | −3.56669 | −0.200642 | ||||||||
\(317\) | −10.6283 | + | 18.4088i | −0.596945 | + | 1.03394i | 0.396324 | + | 0.918111i | \(0.370286\pi\) |
−0.993269 | + | 0.115829i | \(0.963048\pi\) | |||||||
\(318\) | 0.680749 | + | 1.17909i | 0.0381745 | + | 0.0661202i | ||||
\(319\) | −10.4950 | − | 18.1779i | −0.587609 | − | 1.01777i | ||||
\(320\) | 1.79990 | − | 3.11751i | 0.100617 | − | 0.174274i | ||||
\(321\) | −22.5392 | −1.25802 | ||||||||
\(322\) | −2.57027 | − | 0.627473i | −0.143235 | − | 0.0349677i | ||||
\(323\) | 25.5013 | 1.41893 | ||||||||
\(324\) | −11.1442 | + | 19.3024i | −0.619123 | + | 1.07235i | ||||
\(325\) | −3.71080 | − | 6.42730i | −0.205838 | − | 0.356522i | ||||
\(326\) | −7.48650 | − | 12.9670i | −0.414639 | − | 0.718176i | ||||
\(327\) | −20.4191 | + | 35.3670i | −1.12918 | + | 1.95580i | ||||
\(328\) | −2.51655 | −0.138953 | ||||||||
\(329\) | −5.39015 | − | 18.4558i | −0.297169 | − | 1.01750i | ||||
\(330\) | −47.1537 | −2.59573 | ||||||||
\(331\) | 12.0724 | − | 20.9101i | 0.663561 | − | 1.14932i | −0.316112 | − | 0.948722i | \(-0.602377\pi\) |
0.979673 | − | 0.200600i | \(-0.0642892\pi\) | |||||||
\(332\) | 6.22735 | + | 10.7861i | 0.341770 | + | 0.591964i | ||||
\(333\) | −3.85449 | − | 6.67617i | −0.211225 | − | 0.365852i | ||||
\(334\) | −2.54075 | + | 4.40070i | −0.139023 | + | 0.240796i | ||||
\(335\) | 17.1311 | 0.935970 | ||||||||
\(336\) | −5.86595 | + | 6.13427i | −0.320014 | + | 0.334652i | ||||
\(337\) | −7.45947 | −0.406343 | −0.203172 | − | 0.979143i | \(-0.565125\pi\) | ||||
−0.203172 | + | 0.979143i | \(0.565125\pi\) | |||||||
\(338\) | 6.06518 | − | 10.5052i | 0.329903 | − | 0.571408i | ||||
\(339\) | −10.0630 | − | 17.4296i | −0.546548 | − | 0.946648i | ||||
\(340\) | 11.4298 | + | 19.7971i | 0.619870 | + | 1.07365i | ||||
\(341\) | 3.12844 | − | 5.41861i | 0.169414 | − | 0.293434i | ||||
\(342\) | 29.2800 | 1.58328 | ||||||||
\(343\) | −13.9440 | − | 12.1887i | −0.752904 | − | 0.658130i | ||||
\(344\) | 0.532330 | 0.0287013 | ||||||||
\(345\) | −5.77406 | + | 10.0010i | −0.310865 | + | 0.538433i | ||||
\(346\) | 6.01245 | + | 10.4139i | 0.323231 | + | 0.559853i | ||||
\(347\) | 8.23903 | + | 14.2704i | 0.442294 | + | 0.766076i | 0.997859 | − | 0.0653970i | \(-0.0208314\pi\) |
−0.555565 | + | 0.831473i | \(0.687498\pi\) | |||||||
\(348\) | −8.24541 | + | 14.2815i | −0.442000 | + | 0.765567i | ||||
\(349\) | −20.1896 | −1.08073 | −0.540363 | − | 0.841432i | \(-0.681713\pi\) | ||||
−0.540363 | + | 0.841432i | \(0.681713\pi\) | |||||||
\(350\) | 14.5524 | − | 15.2181i | 0.777860 | − | 0.813440i | ||||
\(351\) | −12.8376 | −0.685220 | ||||||||
\(352\) | 2.04162 | − | 3.53619i | 0.108819 | − | 0.188480i | ||||
\(353\) | 11.6707 | + | 20.2142i | 0.621168 | + | 1.07589i | 0.989269 | + | 0.146109i | \(0.0466750\pi\) |
−0.368100 | + | 0.929786i | \(0.619992\pi\) | |||||||
\(354\) | −1.23359 | − | 2.13665i | −0.0655648 | − | 0.113562i | ||||
\(355\) | −10.4947 | + | 18.1773i | −0.557000 | + | 0.964752i | ||||
\(356\) | −10.9827 | −0.582081 | ||||||||
\(357\) | −15.1102 | − | 51.7370i | −0.799717 | − | 2.73821i | ||||
\(358\) | −7.98983 | −0.422276 | ||||||||
\(359\) | −1.68117 | + | 2.91188i | −0.0887289 | + | 0.153683i | −0.906974 | − | 0.421186i | \(-0.861614\pi\) |
0.818245 | + | 0.574869i | \(0.194947\pi\) | |||||||
\(360\) | 13.1235 | + | 22.7305i | 0.691667 | + | 1.19800i | ||||
\(361\) | 1.43675 | + | 2.48852i | 0.0756183 | + | 0.130975i | ||||
\(362\) | −0.262723 | + | 0.455050i | −0.0138084 | + | 0.0239169i | ||||
\(363\) | −18.1985 | −0.955175 | ||||||||
\(364\) | −2.39688 | − | 0.585144i | −0.125631 | − | 0.0306699i | ||||
\(365\) | 41.0283 | 2.14752 | ||||||||
\(366\) | 18.8200 | − | 32.5972i | 0.983737 | − | 1.70388i | ||||
\(367\) | 1.32918 | + | 2.30220i | 0.0693824 | + | 0.120174i | 0.898630 | − | 0.438708i | \(-0.144564\pi\) |
−0.829247 | + | 0.558882i | \(0.811230\pi\) | |||||||
\(368\) | −0.500000 | − | 0.866025i | −0.0260643 | − | 0.0451447i | ||||
\(369\) | 9.17438 | − | 15.8905i | 0.477599 | − | 0.827226i | ||||
\(370\) | −3.80604 | −0.197866 | ||||||||
\(371\) | −1.09084 | − | 0.266305i | −0.0566337 | − | 0.0138258i | ||||
\(372\) | −4.91571 | −0.254868 | ||||||||
\(373\) | −12.4062 | + | 21.4881i | −0.642367 | + | 1.11261i | 0.342535 | + | 0.939505i | \(0.388714\pi\) |
−0.984903 | + | 0.173108i | \(0.944619\pi\) | |||||||
\(374\) | 12.9649 | + | 22.4558i | 0.670397 | + | 1.16116i | ||||
\(375\) | −17.0825 | − | 29.5877i | −0.882135 | − | 1.52790i | ||||
\(376\) | 3.63352 | − | 6.29344i | 0.187384 | − | 0.324559i | ||||
\(377\) | −4.79375 | −0.246891 | ||||||||
\(378\) | −10.2108 | − | 34.9616i | −0.525187 | − | 1.79823i | ||||
\(379\) | 8.02490 | 0.412211 | 0.206106 | − | 0.978530i | \(-0.433921\pi\) | ||||
0.206106 | + | 0.978530i | \(0.433921\pi\) | |||||||
\(380\) | 7.22799 | − | 12.5192i | 0.370788 | − | 0.642223i | ||||
\(381\) | 11.1895 | + | 19.3808i | 0.573257 | + | 0.992910i | ||||
\(382\) | 2.46778 | + | 4.27432i | 0.126263 | + | 0.218693i | ||||
\(383\) | −1.60796 | + | 2.78508i | −0.0821632 | + | 0.142311i | −0.904179 | − | 0.427154i | \(-0.859516\pi\) |
0.822016 | + | 0.569465i | \(0.192850\pi\) | |||||||
\(384\) | −3.20800 | −0.163707 | ||||||||
\(385\) | 26.8774 | − | 28.1068i | 1.36980 | − | 1.43245i | ||||
\(386\) | −8.72476 | −0.444079 | ||||||||
\(387\) | −1.94067 | + | 3.36134i | −0.0986499 | + | 0.170867i | ||||
\(388\) | −8.22097 | − | 14.2391i | −0.417357 | − | 0.722883i | ||||
\(389\) | −1.79036 | − | 3.10100i | −0.0907750 | − | 0.157227i | 0.817062 | − | 0.576549i | \(-0.195601\pi\) |
−0.907837 | + | 0.419322i | \(0.862268\pi\) | |||||||
\(390\) | −5.38454 | + | 9.32629i | −0.272657 | + | 0.472255i | ||||
\(391\) | 6.35028 | 0.321148 | ||||||||
\(392\) | −0.312869 | − | 6.99300i | −0.0158023 | − | 0.353200i | ||||
\(393\) | 27.0255 | 1.36325 | ||||||||
\(394\) | 7.12066 | − | 12.3333i | 0.358733 | − | 0.621345i | ||||
\(395\) | −6.41967 | − | 11.1192i | −0.323009 | − | 0.559468i | ||||
\(396\) | 14.8859 | + | 25.7832i | 0.748047 | + | 1.29566i | ||||
\(397\) | 1.41750 | − | 2.45518i | 0.0711424 | − | 0.123222i | −0.828260 | − | 0.560344i | \(-0.810669\pi\) |
0.899402 | + | 0.437122i | \(0.144002\pi\) | |||||||
\(398\) | −13.7200 | −0.687721 | ||||||||
\(399\) | −23.5564 | + | 24.6339i | −1.17929 | + | 1.23324i | ||||
\(400\) | 7.95849 | 0.397924 | ||||||||
\(401\) | 13.3428 | − | 23.1104i | 0.666308 | − | 1.15408i | −0.312620 | − | 0.949878i | \(-0.601207\pi\) |
0.978929 | − | 0.204202i | \(-0.0654599\pi\) | |||||||
\(402\) | −7.63328 | − | 13.2212i | −0.380713 | − | 0.659415i | ||||
\(403\) | −0.714479 | − | 1.23751i | −0.0355908 | − | 0.0616450i | ||||
\(404\) | −8.55232 | + | 14.8131i | −0.425494 | + | 0.736977i | ||||
\(405\) | −80.2337 | −3.98684 | ||||||||
\(406\) | −3.81287 | − | 13.0552i | −0.189230 | − | 0.647918i | ||||
\(407\) | −4.31719 | −0.213995 | ||||||||
\(408\) | 10.1858 | − | 17.6424i | 0.504274 | − | 0.873429i | ||||
\(409\) | −9.01234 | − | 15.6098i | −0.445632 | − | 0.771856i | 0.552464 | − | 0.833536i | \(-0.313688\pi\) |
−0.998096 | + | 0.0616800i | \(0.980354\pi\) | |||||||
\(410\) | −4.52952 | − | 7.84536i | −0.223697 | − | 0.387455i | ||||
\(411\) | 17.3107 | − | 29.9830i | 0.853874 | − | 1.47895i | ||||
\(412\) | −13.4992 | −0.665060 | ||||||||
\(413\) | 1.97673 | + | 0.482574i | 0.0972684 | + | 0.0237459i | ||||
\(414\) | 7.29124 | 0.358345 | ||||||||
\(415\) | −22.4172 | + | 38.8277i | −1.10042 | + | 1.90597i | ||||
\(416\) | −0.466270 | − | 0.807603i | −0.0228608 | − | 0.0395960i | ||||
\(417\) | −12.6041 | − | 21.8310i | −0.617226 | − | 1.06907i | ||||
\(418\) | 8.19870 | − | 14.2006i | 0.401012 | − | 0.694573i | ||||
\(419\) | 0.704693 | 0.0344265 | 0.0172133 | − | 0.999852i | \(-0.494521\pi\) | ||||
0.0172133 | + | 0.999852i | \(0.494521\pi\) | |||||||
\(420\) | −29.6817 | − | 7.24613i | −1.44832 | − | 0.353575i | ||||
\(421\) | 10.2408 | 0.499107 | 0.249554 | − | 0.968361i | \(-0.419716\pi\) | ||||
0.249554 | + | 0.968361i | \(0.419716\pi\) | |||||||
\(422\) | −0.982052 | + | 1.70096i | −0.0478055 | + | 0.0828016i | ||||
\(423\) | 26.4929 | + | 45.8870i | 1.28813 | + | 2.23110i | ||||
\(424\) | −0.212204 | − | 0.367548i | −0.0103055 | − | 0.0178497i | ||||
\(425\) | −25.2693 | + | 43.7678i | −1.22574 | + | 2.12305i | ||||
\(426\) | 18.7049 | 0.906256 | ||||||||
\(427\) | 8.70280 | + | 29.7982i | 0.421158 | + | 1.44204i | ||||
\(428\) | 7.02595 | 0.339612 | ||||||||
\(429\) | −6.10768 | + | 10.5788i | −0.294882 | + | 0.510750i | ||||
\(430\) | 0.958138 | + | 1.65954i | 0.0462055 | + | 0.0800303i | ||||
\(431\) | 16.4745 | + | 28.5347i | 0.793549 | + | 1.37447i | 0.923756 | + | 0.382981i | \(0.125102\pi\) |
−0.130207 | + | 0.991487i | \(0.541564\pi\) | |||||||
\(432\) | 6.88314 | − | 11.9219i | 0.331165 | − | 0.573595i | ||||
\(433\) | 24.7235 | 1.18814 | 0.594068 | − | 0.804415i | \(-0.297521\pi\) | ||||
0.594068 | + | 0.804415i | \(0.297521\pi\) | |||||||
\(434\) | 2.80193 | − | 2.93009i | 0.134497 | − | 0.140649i | ||||
\(435\) | −59.3635 | −2.84626 | ||||||||
\(436\) | 6.36508 | − | 11.0246i | 0.304832 | − | 0.527985i | ||||
\(437\) | −2.00789 | − | 3.47777i | −0.0960505 | − | 0.166364i | ||||
\(438\) | −18.2814 | − | 31.6644i | −0.873520 | − | 1.51298i | ||||
\(439\) | 7.30561 | − | 12.6537i | 0.348678 | − | 0.603928i | −0.637337 | − | 0.770585i | \(-0.719964\pi\) |
0.986015 | + | 0.166657i | \(0.0532974\pi\) | |||||||
\(440\) | 14.6988 | 0.700738 | ||||||||
\(441\) | 45.2972 | + | 23.5183i | 2.15701 | + | 1.11992i | ||||
\(442\) | 5.92189 | 0.281676 | ||||||||
\(443\) | 10.6276 | − | 18.4075i | 0.504931 | − | 0.874566i | −0.495053 | − | 0.868863i | \(-0.664851\pi\) |
0.999984 | − | 0.00570286i | \(-0.00181529\pi\) | |||||||
\(444\) | 1.69590 | + | 2.93738i | 0.0804837 | + | 0.139402i | ||||
\(445\) | −19.7677 | − | 34.2386i | −0.937078 | − | 1.62307i | ||||
\(446\) | −3.50333 | + | 6.06795i | −0.165888 | + | 0.287326i | ||||
\(447\) | 33.5809 | 1.58832 | ||||||||
\(448\) | 1.82854 | − | 1.91218i | 0.0863905 | − | 0.0903420i | ||||
\(449\) | −30.0560 | −1.41843 | −0.709215 | − | 0.704993i | \(-0.750950\pi\) | ||||
−0.709215 | + | 0.704993i | \(0.750950\pi\) | |||||||
\(450\) | −29.0136 | + | 50.2531i | −1.36771 | + | 2.36895i | ||||
\(451\) | −5.13784 | − | 8.89900i | −0.241931 | − | 0.419037i | ||||
\(452\) | 3.13685 | + | 5.43319i | 0.147545 | + | 0.255556i | ||||
\(453\) | 8.39320 | − | 14.5375i | 0.394347 | − | 0.683029i | ||||
\(454\) | −25.1397 | −1.17986 | ||||||||
\(455\) | −2.48994 | − | 8.52549i | −0.116730 | − | 0.399681i | ||||
\(456\) | −12.8826 | −0.603284 | ||||||||
\(457\) | −1.48247 | + | 2.56771i | −0.0693469 | + | 0.120112i | −0.898614 | − | 0.438740i | \(-0.855425\pi\) |
0.829267 | + | 0.558852i | \(0.188758\pi\) | |||||||
\(458\) | 7.92118 | + | 13.7199i | 0.370133 | + | 0.641089i | ||||
\(459\) | 43.7099 | + | 75.7077i | 2.04020 | + | 3.53373i | ||||
\(460\) | 1.79990 | − | 3.11751i | 0.0839205 | − | 0.145355i | ||||
\(461\) | −16.1609 | −0.752687 | −0.376343 | − | 0.926480i | \(-0.622819\pi\) | ||||
−0.376343 | + | 0.926480i | \(0.622819\pi\) | |||||||
\(462\) | −33.6680 | − | 8.21929i | −1.56638 | − | 0.382396i | ||||
\(463\) | −32.1830 | −1.49567 | −0.747835 | − | 0.663885i | \(-0.768906\pi\) | ||||
−0.747835 | + | 0.663885i | \(0.768906\pi\) | |||||||
\(464\) | 2.57027 | − | 4.45183i | 0.119322 | − | 0.206671i | ||||
\(465\) | −8.84776 | − | 15.3248i | −0.410305 | − | 0.710669i | ||||
\(466\) | −2.56249 | − | 4.43836i | −0.118705 | − | 0.205603i | ||||
\(467\) | 1.84930 | − | 3.20308i | 0.0855753 | − | 0.148221i | −0.820061 | − | 0.572276i | \(-0.806061\pi\) |
0.905636 | + | 0.424055i | \(0.139394\pi\) | |||||||
\(468\) | 6.79937 | 0.314301 | ||||||||
\(469\) | 12.2317 | + | 2.98609i | 0.564806 | + | 0.137885i | ||||
\(470\) | 26.1598 | 1.20666 | ||||||||
\(471\) | −31.5806 | + | 54.6991i | −1.45515 | + | 2.52040i | ||||
\(472\) | 0.384537 | + | 0.666038i | 0.0176998 | + | 0.0306569i | ||||
\(473\) | 1.08682 | + | 1.88242i | 0.0499718 | + | 0.0865538i | ||||
\(474\) | −5.72097 | + | 9.90901i | −0.262773 | + | 0.455136i | ||||
\(475\) | 31.9596 | 1.46640 | ||||||||
\(476\) | 4.71017 | + | 16.1275i | 0.215890 | + | 0.739204i | ||||
\(477\) | 3.09446 | 0.141686 | ||||||||
\(478\) | 6.60347 | − | 11.4376i | 0.302036 | − | 0.523141i | ||||
\(479\) | 18.7783 | + | 32.5249i | 0.858001 | + | 1.48610i | 0.873833 | + | 0.486226i | \(0.161627\pi\) |
−0.0158322 | + | 0.999875i | \(0.505040\pi\) | |||||||
\(480\) | −5.77406 | − | 10.0010i | −0.263548 | − | 0.456479i | ||||
\(481\) | −0.492984 | + | 0.853874i | −0.0224781 | + | 0.0389333i | ||||
\(482\) | 27.6622 | 1.25998 | ||||||||
\(483\) | −5.86595 | + | 6.13427i | −0.266910 | + | 0.279119i | ||||
\(484\) | 5.67287 | 0.257858 | ||||||||
\(485\) | 29.5938 | − | 51.2579i | 1.34378 | − | 2.32750i | ||||
\(486\) | 15.1012 | + | 26.1560i | 0.685004 | + | 1.18646i | ||||
\(487\) | 8.87829 | + | 15.3777i | 0.402314 | + | 0.696828i | 0.994005 | − | 0.109337i | \(-0.0348727\pi\) |
−0.591691 | + | 0.806165i | \(0.701539\pi\) | |||||||
\(488\) | −5.86659 | + | 10.1612i | −0.265568 | + | 0.459977i | ||||
\(489\) | −48.0333 | −2.17214 | ||||||||
\(490\) | 21.2376 | − | 13.5620i | 0.959418 | − | 0.612671i | ||||
\(491\) | 6.93794 | 0.313105 | 0.156552 | − | 0.987670i | \(-0.449962\pi\) | ||||
0.156552 | + | 0.987670i | \(0.449962\pi\) | |||||||
\(492\) | −4.03654 | + | 6.99149i | −0.181981 | + | 0.315201i | ||||
\(493\) | 16.3219 | + | 28.2704i | 0.735103 | + | 1.27324i | ||||
\(494\) | −1.87244 | − | 3.24316i | −0.0842450 | − | 0.145917i | ||||
\(495\) | −53.5863 | + | 92.8142i | −2.40852 | + | 4.17169i | ||||
\(496\) | 1.53233 | 0.0688036 | ||||||||
\(497\) | −10.6617 | + | 11.1494i | −0.478243 | + | 0.500118i | ||||
\(498\) | 39.9546 | 1.79041 | ||||||||
\(499\) | 2.79593 | − | 4.84269i | 0.125163 | − | 0.216789i | −0.796634 | − | 0.604462i | \(-0.793388\pi\) |
0.921797 | + | 0.387674i | \(0.126721\pi\) | |||||||
\(500\) | 5.32497 | + | 9.22312i | 0.238140 | + | 0.412470i | ||||
\(501\) | 8.15070 | + | 14.1174i | 0.364147 | + | 0.630720i | ||||
\(502\) | −6.91663 | + | 11.9799i | −0.308704 | + | 0.534691i | ||||
\(503\) | −10.1204 | −0.451247 | −0.225624 | − | 0.974215i | \(-0.572442\pi\) | ||||
−0.225624 | + | 0.974215i | \(0.572442\pi\) | |||||||
\(504\) | 5.40810 | + | 18.5172i | 0.240896 | + | 0.824823i | ||||
\(505\) | −61.5731 | −2.73997 | ||||||||
\(506\) | 2.04162 | − | 3.53619i | 0.0907611 | − | 0.157203i | ||||
\(507\) | −19.4571 | − | 33.7007i | −0.864120 | − | 1.49670i | ||||
\(508\) | −3.48801 | − | 6.04141i | −0.154755 | − | 0.268044i | ||||
\(509\) | 12.7225 | − | 22.0360i | 0.563915 | − | 0.976730i | −0.433234 | − | 0.901281i | \(-0.642628\pi\) |
0.997150 | − | 0.0754487i | \(-0.0240389\pi\) | |||||||
\(510\) | 73.3338 | 3.24727 | ||||||||
\(511\) | 29.2944 | + | 7.15157i | 1.29591 | + | 0.316367i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 27.6412 | − | 47.8759i | 1.22039 | − | 2.11377i | ||||
\(514\) | −12.0746 | − | 20.9138i | −0.532587 | − | 0.922468i | ||||
\(515\) | −24.2972 | − | 42.0840i | −1.07066 | − | 1.85444i | ||||
\(516\) | 0.853856 | − | 1.47892i | 0.0375889 | − | 0.0651059i | ||||
\(517\) | 29.6731 | 1.30502 | ||||||||
\(518\) | −2.71753 | − | 0.663424i | −0.119401 | − | 0.0291492i | ||||
\(519\) | 38.5758 | 1.69329 | ||||||||
\(520\) | 1.67847 | − | 2.90720i | 0.0736059 | − | 0.127489i | ||||
\(521\) | −1.88864 | − | 3.27123i | −0.0827430 | − | 0.143315i | 0.821684 | − | 0.569943i | \(-0.193035\pi\) |
−0.904427 | + | 0.426628i | \(0.859701\pi\) | |||||||
\(522\) | 18.7404 | + | 32.4594i | 0.820247 | + | 1.42071i | ||||
\(523\) | 3.60681 | − | 6.24717i | 0.157715 | − | 0.273170i | −0.776330 | − | 0.630327i | \(-0.782921\pi\) |
0.934044 | + | 0.357158i | \(0.116254\pi\) | |||||||
\(524\) | −8.42441 | −0.368022 | ||||||||
\(525\) | −18.9369 | − | 64.8394i | −0.826472 | − | 2.82982i | ||||
\(526\) | 28.3042 | 1.23412 | ||||||||
\(527\) | −4.86536 | + | 8.42706i | −0.211939 | + | 0.367088i | ||||
\(528\) | −6.54951 | − | 11.3441i | −0.285031 | − | 0.493688i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.0217391 | − | 0.0376533i | ||||
\(530\) | 0.763890 | − | 1.32310i | 0.0331812 | − | 0.0574716i | ||||
\(531\) | −5.60751 | −0.243345 | ||||||||
\(532\) | 7.34303 | − | 7.67890i | 0.318361 | − | 0.332923i | ||||
\(533\) | −2.34678 | −0.101650 | ||||||||
\(534\) | −17.6162 | + | 30.5122i | −0.762328 | + | 1.32039i | ||||
\(535\) | 12.6460 | + | 21.9035i | 0.546733 | + | 0.946969i | ||||
\(536\) | 2.37945 | + | 4.12134i | 0.102777 | + | 0.178015i | ||||
\(537\) | −12.8157 | + | 22.1974i | −0.553037 | + | 0.957889i | ||||
\(538\) | −30.2279 | −1.30322 | ||||||||
\(539\) | 24.0898 | − | 15.3834i | 1.03762 | − | 0.662611i | ||||
\(540\) | 49.5557 | 2.13254 | ||||||||
\(541\) | 5.19997 | − | 9.00662i | 0.223564 | − | 0.387225i | −0.732323 | − | 0.680957i | \(-0.761564\pi\) |
0.955888 | + | 0.293732i | \(0.0948974\pi\) | |||||||
\(542\) | 4.57665 | + | 7.92699i | 0.196584 | + | 0.340493i | ||||
\(543\) | 0.842814 | + | 1.45980i | 0.0361686 | + | 0.0626459i | ||||
\(544\) | −3.17514 | + | 5.49951i | −0.136133 | + | 0.235789i | ||||
\(545\) | 45.8259 | 1.96297 | ||||||||
\(546\) | −5.47024 | + | 5.72045i | −0.234105 | + | 0.244813i | ||||
\(547\) | 24.3221 | 1.03994 | 0.519969 | − | 0.854185i | \(-0.325943\pi\) | ||||
0.519969 | + | 0.854185i | \(0.325943\pi\) | |||||||
\(548\) | −5.39611 | + | 9.34634i | −0.230510 | + | 0.399256i | ||||
\(549\) | −42.7747 | − | 74.0879i | −1.82558 | − | 3.16200i | ||||
\(550\) | 16.2482 | + | 28.1427i | 0.692826 | + | 1.20001i | ||||
\(551\) | 10.3216 | − | 17.8776i | 0.439716 | − | 0.761611i | ||||
\(552\) | −3.20800 | −0.136541 | ||||||||
\(553\) | −2.64551 | − | 9.05817i | −0.112499 | − | 0.385193i | ||||
\(554\) | 18.8544 | 0.801048 | ||||||||
\(555\) | −6.10487 | + | 10.5740i | −0.259137 | + | 0.448839i | ||||
\(556\) | 3.92897 | + | 6.80517i | 0.166625 | + | 0.288603i | ||||
\(557\) | 2.24618 | + | 3.89049i | 0.0951735 | + | 0.164845i | 0.909681 | − | 0.415308i | \(-0.136326\pi\) |
−0.814508 | + | 0.580153i | \(0.802993\pi\) | |||||||
\(558\) | −5.58629 | + | 9.67574i | −0.236487 | + | 0.409607i | ||||
\(559\) | 0.496419 | 0.0209963 | ||||||||
\(560\) | 9.25242 | + | 2.25877i | 0.390986 | + | 0.0954506i | ||||
\(561\) | 83.1825 | 3.51197 | ||||||||
\(562\) | −6.05880 | + | 10.4942i | −0.255575 | + | 0.442669i | ||||
\(563\) | −19.5361 | − | 33.8376i | −0.823349 | − | 1.42608i | −0.903174 | − | 0.429274i | \(-0.858769\pi\) |
0.0798249 | − | 0.996809i | \(-0.474564\pi\) | |||||||
\(564\) | −11.6563 | − | 20.1893i | −0.490820 | − | 0.850124i | ||||
\(565\) | −11.2920 | + | 19.5583i | −0.475058 | + | 0.822825i | ||||
\(566\) | −13.2093 | −0.555227 | ||||||||
\(567\) | −57.2873 | − | 13.9854i | −2.40584 | − | 0.587332i | ||||
\(568\) | −5.83072 | −0.244651 | ||||||||
\(569\) | −4.66357 | + | 8.07755i | −0.195507 | + | 0.338628i | −0.947067 | − | 0.321037i | \(-0.895969\pi\) |
0.751559 | + | 0.659665i | \(0.229302\pi\) | |||||||
\(570\) | −23.1873 | − | 40.1617i | −0.971211 | − | 1.68219i | ||||
\(571\) | 14.5593 | + | 25.2175i | 0.609289 | + | 1.05532i | 0.991358 | + | 0.131186i | \(0.0418785\pi\) |
−0.382069 | + | 0.924134i | \(0.624788\pi\) | |||||||
\(572\) | 1.90389 | − | 3.29764i | 0.0796058 | − | 0.137881i | ||||
\(573\) | 15.8333 | 0.661444 | ||||||||
\(574\) | −1.86659 | − | 6.39116i | −0.0779099 | − | 0.266762i | ||||
\(575\) | 7.95849 | 0.331892 | ||||||||
\(576\) | −3.64562 | + | 6.31440i | −0.151901 | + | 0.263100i | ||||
\(577\) | 4.97364 | + | 8.61459i | 0.207055 | + | 0.358630i | 0.950786 | − | 0.309850i | \(-0.100279\pi\) |
−0.743730 | + | 0.668480i | \(0.766945\pi\) | |||||||
\(578\) | −11.6630 | − | 20.2010i | −0.485119 | − | 0.840250i | ||||
\(579\) | −13.9945 | + | 24.2392i | −0.581592 | + | 1.00735i | ||||
\(580\) | 18.5048 | 0.768372 | ||||||||
\(581\) | −22.7739 | + | 23.8156i | −0.944823 | + | 0.988039i | ||||
\(582\) | −52.7457 | −2.18638 | ||||||||
\(583\) | 0.866480 | − | 1.50079i | 0.0358859 | − | 0.0621563i | ||||
\(584\) | 5.69870 | + | 9.87045i | 0.235814 | + | 0.408442i | ||||
\(585\) | 12.2382 | + | 21.1971i | 0.505985 | + | 0.876392i | ||||
\(586\) | −7.43622 | + | 12.8799i | −0.307188 | + | 0.532064i | ||||
\(587\) | 28.5555 | 1.17861 | 0.589305 | − | 0.807910i | \(-0.299402\pi\) | ||||
0.589305 | + | 0.807910i | \(0.299402\pi\) | |||||||
\(588\) | −19.9298 | − | 10.3476i | −0.821893 | − | 0.426726i | ||||
\(589\) | 6.15350 | 0.253551 | ||||||||
\(590\) | −1.38425 | + | 2.39760i | −0.0569888 | + | 0.0987075i | ||||
\(591\) | −22.8430 | − | 39.5653i | −0.939637 | − | 1.62750i | ||||
\(592\) | −0.528647 | − | 0.915643i | −0.0217273 | − | 0.0376327i | ||||
\(593\) | 13.1399 | − | 22.7589i | 0.539590 | − | 0.934598i | −0.459336 | − | 0.888263i | \(-0.651913\pi\) |
0.998926 | − | 0.0463349i | \(-0.0147541\pi\) | |||||||
\(594\) | 56.2110 | 2.30637 | ||||||||
\(595\) | −41.7999 | + | 43.7118i | −1.71363 | + | 1.79201i | ||||
\(596\) | −10.4679 | −0.428781 | ||||||||
\(597\) | −22.0068 | + | 38.1170i | −0.900680 | + | 1.56002i | ||||
\(598\) | −0.466270 | − | 0.807603i | −0.0190672 | − | 0.0330254i | ||||
\(599\) | 14.4809 | + | 25.0816i | 0.591673 | + | 1.02481i | 0.994007 | + | 0.109315i | \(0.0348658\pi\) |
−0.402334 | + | 0.915493i | \(0.631801\pi\) | |||||||
\(600\) | 12.7654 | − | 22.1103i | 0.521145 | − | 0.902650i | ||||
\(601\) | 2.92666 | 0.119381 | 0.0596905 | − | 0.998217i | \(-0.480989\pi\) | ||||
0.0596905 | + | 0.998217i | \(0.480989\pi\) | |||||||
\(602\) | 0.394843 | + | 1.35193i | 0.0160926 | + | 0.0551007i | ||||
\(603\) | −34.6983 | −1.41303 | ||||||||
\(604\) | −2.61634 | + | 4.53163i | −0.106457 | + | 0.184389i | ||||
\(605\) | 10.2106 | + | 17.6852i | 0.415118 | + | 0.719006i | ||||
\(606\) | 27.4358 | + | 47.5202i | 1.11450 | + | 1.93038i | ||||
\(607\) | 11.7275 | − | 20.3126i | 0.476003 | − | 0.824461i | −0.523619 | − | 0.851952i | \(-0.675418\pi\) |
0.999622 | + | 0.0274912i | \(0.00875182\pi\) | |||||||
\(608\) | 4.01578 | 0.162861 | ||||||||
\(609\) | −42.3858 | − | 10.3476i | −1.71756 | − | 0.419304i | ||||
\(610\) | −42.2370 | −1.71013 | ||||||||
\(611\) | 3.38840 | − | 5.86888i | 0.137080 | − | 0.237430i | ||||
\(612\) | −23.1507 | − | 40.0982i | −0.935812 | − | 1.62087i | ||||
\(613\) | −2.64054 | − | 4.57354i | −0.106650 | − | 0.184724i | 0.807761 | − | 0.589510i | \(-0.200679\pi\) |
−0.914411 | + | 0.404786i | \(0.867346\pi\) | |||||||
\(614\) | 5.33363 | − | 9.23811i | 0.215248 | − | 0.372820i | ||||
\(615\) | −29.0614 | −1.17187 | ||||||||
\(616\) | 10.4950 | + | 2.56213i | 0.422857 | + | 0.103231i | ||||
\(617\) | 7.69908 | 0.309953 | 0.154977 | − | 0.987918i | \(-0.450470\pi\) | ||||
0.154977 | + | 0.987918i | \(0.450470\pi\) | |||||||
\(618\) | −21.6527 | + | 37.5037i | −0.871001 | + | 1.50862i | ||||
\(619\) | 7.09751 | + | 12.2933i | 0.285273 | + | 0.494108i | 0.972675 | − | 0.232169i | \(-0.0745823\pi\) |
−0.687402 | + | 0.726277i | \(0.741249\pi\) | |||||||
\(620\) | 2.75803 | + | 4.77705i | 0.110765 | + | 0.191851i | ||||
\(621\) | 6.88314 | − | 11.9219i | 0.276211 | − | 0.478411i | ||||
\(622\) | −16.9122 | −0.678118 | ||||||||
\(623\) | −8.14614 | − | 27.8922i | −0.326368 | − | 1.11748i | ||||
\(624\) | −2.99158 | −0.119759 | ||||||||
\(625\) | 0.727453 | − | 1.25999i | 0.0290981 | − | 0.0503995i | ||||
\(626\) | −13.2189 | − | 22.8959i | −0.528335 | − | 0.915103i | ||||
\(627\) | −26.3014 | − | 45.5554i | −1.05038 | − | 1.81931i | ||||
\(628\) | 9.84432 | − | 17.0509i | 0.392831 | − | 0.680404i | ||||
\(629\) | 6.71411 | 0.267709 | ||||||||
\(630\) | −47.9936 | + | 50.1889i | −1.91211 | + | 1.99957i | ||||
\(631\) | −7.60667 | −0.302817 | −0.151408 | − | 0.988471i | \(-0.548381\pi\) | ||||
−0.151408 | + | 0.988471i | \(0.548381\pi\) | |||||||
\(632\) | 1.78335 | − | 3.08885i | 0.0709377 | − | 0.122868i | ||||
\(633\) | 3.15042 | + | 5.45668i | 0.125218 | + | 0.216884i | ||||
\(634\) | −10.6283 | − | 18.4088i | −0.422104 | − | 0.731105i | ||||
\(635\) | 12.5561 | − | 21.7478i | 0.498274 | − | 0.863036i | ||||
\(636\) | −1.36150 | −0.0539869 | ||||||||
\(637\) | −0.291763 | − | 6.52126i | −0.0115601 | − | 0.258382i | ||||
\(638\) | 20.9901 | 0.831004 | ||||||||
\(639\) | 21.2566 | − | 36.8175i | 0.840897 | − | 1.45648i | ||||
\(640\) | 1.79990 | + | 3.11751i | 0.0711471 | + | 0.123230i | ||||
\(641\) | −4.24057 | − | 7.34488i | −0.167492 | − | 0.290105i | 0.770045 | − | 0.637989i | \(-0.220234\pi\) |
−0.937538 | + | 0.347884i | \(0.886900\pi\) | |||||||
\(642\) | 11.2696 | − | 19.5195i | 0.444776 | − | 0.770374i | ||||
\(643\) | 18.9051 | 0.745543 | 0.372771 | − | 0.927923i | \(-0.378408\pi\) | ||||
0.372771 | + | 0.927923i | \(0.378408\pi\) | |||||||
\(644\) | 1.82854 | − | 1.91218i | 0.0720546 | − | 0.0753505i | ||||
\(645\) | 6.14740 | 0.242054 | ||||||||
\(646\) | −12.7507 | + | 22.0848i | −0.501669 | + | 0.868915i | ||||
\(647\) | 5.53730 | + | 9.59089i | 0.217694 | + | 0.377057i | 0.954103 | − | 0.299480i | \(-0.0968132\pi\) |
−0.736409 | + | 0.676537i | \(0.763480\pi\) | |||||||
\(648\) | −11.1442 | − | 19.3024i | −0.437786 | − | 0.758268i | ||||
\(649\) | −1.57016 | + | 2.71959i | −0.0616341 | + | 0.106753i | ||||
\(650\) | 7.42161 | 0.291099 | ||||||||
\(651\) | −3.64611 | − | 12.4842i | −0.142902 | − | 0.489294i | ||||
\(652\) | 14.9730 | 0.586388 | ||||||||
\(653\) | 11.8858 | − | 20.5869i | 0.465129 | − | 0.805627i | −0.534079 | − | 0.845435i | \(-0.679341\pi\) |
0.999207 | + | 0.0398083i | \(0.0126747\pi\) | |||||||
\(654\) | −20.4191 | − | 35.3670i | −0.798452 | − | 1.38296i | ||||
\(655\) | −15.1630 | − | 26.2632i | −0.592469 | − | 1.02619i | ||||
\(656\) | 1.25827 | − | 2.17939i | 0.0491273 | − | 0.0850911i | ||||
\(657\) | −83.1012 | −3.24209 | ||||||||
\(658\) | 18.6782 | + | 4.55987i | 0.728154 | + | 0.177762i | ||||
\(659\) | 7.07118 | 0.275454 | 0.137727 | − | 0.990470i | \(-0.456020\pi\) | ||||
0.137727 | + | 0.990470i | \(0.456020\pi\) | |||||||
\(660\) | 23.5769 | − | 40.8363i | 0.917728 | − | 1.58955i | ||||
\(661\) | −4.53948 | − | 7.86261i | −0.176565 | − | 0.305820i | 0.764137 | − | 0.645054i | \(-0.223165\pi\) |
−0.940702 | + | 0.339235i | \(0.889832\pi\) | |||||||
\(662\) | 12.0724 | + | 20.9101i | 0.469209 | + | 0.812693i | ||||
\(663\) | 9.49870 | − | 16.4522i | 0.368899 | − | 0.638952i | ||||
\(664\) | −12.4547 | −0.483336 | ||||||||
\(665\) | 37.1557 | + | 9.07074i | 1.44084 | + | 0.351748i | ||||
\(666\) | 7.70898 | 0.298717 | ||||||||
\(667\) | 2.57027 | − | 4.45183i | 0.0995212 | − | 0.172376i | ||||
\(668\) | −2.54075 | − | 4.40070i | −0.0983044 | − | 0.170268i | ||||
\(669\) | 11.2387 | + | 19.4660i | 0.434512 | + | 0.752597i | ||||
\(670\) | −8.56553 | + | 14.8359i | −0.330915 | + | 0.573162i | ||||
\(671\) | −47.9094 | −1.84952 | ||||||||
\(672\) | −2.37945 | − | 8.14720i | −0.0917894 | − | 0.314285i | ||||
\(673\) | −49.4544 | −1.90633 | −0.953164 | − | 0.302453i | \(-0.902194\pi\) | ||||
−0.953164 | + | 0.302453i | \(0.902194\pi\) | |||||||
\(674\) | 3.72974 | − | 6.46009i | 0.143664 | − | 0.248833i | ||||
\(675\) | 54.7794 | + | 94.8806i | 2.10846 | + | 3.65196i | ||||
\(676\) | 6.06518 | + | 10.5052i | 0.233276 | + | 0.404046i | ||||
\(677\) | −16.2963 | + | 28.2261i | −0.626319 | + | 1.08482i | 0.361966 | + | 0.932191i | \(0.382106\pi\) |
−0.988284 | + | 0.152624i | \(0.951228\pi\) | |||||||
\(678\) | 20.1260 | 0.772935 | ||||||||
\(679\) | 30.0648 | − | 31.4400i | 1.15378 | − | 1.20655i | ||||
\(680\) | −22.8597 | −0.876629 | ||||||||
\(681\) | −40.3240 | + | 69.8433i | −1.54522 | + | 2.67640i | ||||
\(682\) | 3.12844 | + | 5.41861i | 0.119794 | + | 0.207489i | ||||
\(683\) | −16.4157 | − | 28.4328i | −0.628130 | − | 1.08795i | −0.987927 | − | 0.154922i | \(-0.950487\pi\) |
0.359797 | − | 0.933031i | \(-0.382846\pi\) | |||||||
\(684\) | −14.6400 | + | 25.3572i | −0.559775 | + | 0.969558i | ||||
\(685\) | −38.8497 | −1.48437 | ||||||||
\(686\) | 17.5277 | − | 5.98147i | 0.669213 | − | 0.228374i | ||||
\(687\) | 50.8223 | 1.93899 | ||||||||
\(688\) | −0.266165 | + | 0.461011i | −0.0101474 | + | 0.0175759i | ||||
\(689\) | −0.197889 | − | 0.342753i | −0.00753896 | − | 0.0130579i | ||||
\(690\) | −5.77406 | − | 10.0010i | −0.219815 | − | 0.380730i | ||||
\(691\) | −19.1784 | + | 33.2180i | −0.729581 | + | 1.26367i | 0.227479 | + | 0.973783i | \(0.426952\pi\) |
−0.957060 | + | 0.289889i | \(0.906382\pi\) | |||||||
\(692\) | −12.0249 | −0.457118 | ||||||||
\(693\) | −54.4391 | + | 56.9292i | −2.06797 | + | 2.16256i | ||||
\(694\) | −16.4781 | −0.625498 | ||||||||
\(695\) | −14.1435 | + | 24.4972i | −0.536492 | + | 0.929231i | ||||
\(696\) | −8.24541 | − | 14.2815i | −0.312541 | − | 0.541338i | ||||
\(697\) | 7.99039 | + | 13.8398i | 0.302658 | + | 0.524219i | ||||
\(698\) | 10.0948 | − | 17.4847i | 0.382094 | − | 0.661807i | ||||
\(699\) | −16.4409 | −0.621852 | ||||||||
\(700\) | 5.90302 | + | 20.2118i | 0.223113 | + | 0.763934i | ||||
\(701\) | −42.6512 | −1.61091 | −0.805457 | − | 0.592654i | \(-0.798080\pi\) | ||||
−0.805457 | + | 0.592654i | \(0.798080\pi\) | |||||||
\(702\) | 6.41880 | − | 11.1177i | 0.242262 | − | 0.419610i | ||||
\(703\) | −2.12293 | − | 3.67702i | −0.0800678 | − | 0.138682i | ||||
\(704\) | 2.04162 | + | 3.53619i | 0.0769465 | + | 0.133275i | ||||
\(705\) | 41.9603 | − | 72.6774i | 1.58032 | − | 2.73719i | ||||
\(706\) | −23.3414 | −0.878465 | ||||||||
\(707\) | −43.9635 | − | 10.7327i | −1.65342 | − | 0.403645i | ||||
\(708\) | 2.46719 | 0.0927226 | ||||||||
\(709\) | −6.36151 | + | 11.0185i | −0.238911 | + | 0.413807i | −0.960402 | − | 0.278617i | \(-0.910124\pi\) |
0.721491 | + | 0.692424i | \(0.243457\pi\) | |||||||
\(710\) | −10.4947 | − | 18.1773i | −0.393858 | − | 0.682182i | ||||
\(711\) | 13.0028 | + | 22.5215i | 0.487643 | + | 0.844623i | ||||
\(712\) | 5.49134 | − | 9.51129i | 0.205797 | − | 0.356450i | ||||
\(713\) | 1.53233 | 0.0573862 | ||||||||
\(714\) | 52.3607 | + | 12.7827i | 1.95955 | + | 0.478380i | ||||
\(715\) | 13.7072 | 0.512621 | ||||||||
\(716\) | 3.99492 | − | 6.91940i | 0.149297 | − | 0.258590i | ||||
\(717\) | −21.1839 | − | 36.6916i | −0.791128 | − | 1.37027i | ||||
\(718\) | −1.68117 | − | 2.91188i | −0.0627408 | − | 0.108670i | ||||
\(719\) | −1.22475 | + | 2.12134i | −0.0456757 | + | 0.0791125i | −0.887959 | − | 0.459922i | \(-0.847877\pi\) |
0.842284 | + | 0.539034i | \(0.181211\pi\) | |||||||
\(720\) | −26.2469 | −0.978165 | ||||||||
\(721\) | −10.0127 | − | 34.2834i | −0.372894 | − | 1.27678i | ||||
\(722\) | −2.87350 | −0.106940 | ||||||||
\(723\) | 44.3701 | − | 76.8513i | 1.65014 | − | 2.85813i | ||||
\(724\) | −0.262723 | − | 0.455050i | −0.00976402 | − | 0.0169118i | ||||
\(725\) | 20.4554 | + | 35.4299i | 0.759696 | + | 1.31583i | ||||
\(726\) | 9.09927 | − | 15.7604i | 0.337705 | − | 0.584923i | ||||
\(727\) | 22.6449 | 0.839853 | 0.419926 | − | 0.907558i | \(-0.362056\pi\) | ||||
0.419926 | + | 0.907558i | \(0.362056\pi\) | |||||||
\(728\) | 1.70519 | − | 1.78318i | 0.0631985 | − | 0.0660892i | ||||
\(729\) | 30.0238 | 1.11199 | ||||||||
\(730\) | −20.5141 | + | 35.5315i | −0.759262 | + | 1.31508i | ||||
\(731\) | −1.69022 | − | 2.92755i | −0.0625151 | − | 0.108279i | ||||
\(732\) | 18.8200 | + | 32.5972i | 0.695607 | + | 1.20483i | ||||
\(733\) | −2.21880 | + | 3.84307i | −0.0819531 | + | 0.141947i | −0.904089 | − | 0.427345i | \(-0.859449\pi\) |
0.822136 | + | 0.569292i | \(0.192782\pi\) | |||||||
\(734\) | −2.65835 | −0.0981216 | ||||||||
\(735\) | −3.61305 | − | 80.7560i | −0.133269 | − | 2.97873i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −9.71589 | + | 16.8284i | −0.357889 | + | 0.619882i | ||||
\(738\) | 9.17438 | + | 15.8905i | 0.337713 | + | 0.584937i | ||||
\(739\) | 18.3038 | + | 31.7031i | 0.673316 | + | 1.16622i | 0.976958 | + | 0.213431i | \(0.0684640\pi\) |
−0.303642 | + | 0.952786i | \(0.598203\pi\) | |||||||
\(740\) | 1.90302 | − | 3.29612i | 0.0699563 | − | 0.121168i | ||||
\(741\) | −12.0135 | −0.441329 | ||||||||
\(742\) | 0.776047 | − | 0.811544i | 0.0284896 | − | 0.0297927i | ||||
\(743\) | −14.2954 | −0.524446 | −0.262223 | − | 0.965007i | \(-0.584456\pi\) | ||||
−0.262223 | + | 0.965007i | \(0.584456\pi\) | |||||||
\(744\) | 2.45785 | − | 4.25713i | 0.0901093 | − | 0.156074i | ||||
\(745\) | −18.8411 | − | 32.6337i | −0.690285 | − | 1.19561i | ||||
\(746\) | −12.4062 | − | 21.4881i | −0.454222 | − | 0.786736i | ||||
\(747\) | 45.4051 | − | 78.6439i | 1.66129 | − | 2.87743i | ||||
\(748\) | −25.9297 | −0.948085 | ||||||||
\(749\) | 5.21133 | + | 17.8435i | 0.190418 | + | 0.651986i | ||||
\(750\) | 34.1650 | 1.24753 | ||||||||
\(751\) | 18.9503 | − | 32.8228i | 0.691505 | − | 1.19772i | −0.279840 | − | 0.960047i | \(-0.590282\pi\) |
0.971345 | − | 0.237675i | \(-0.0763852\pi\) | |||||||
\(752\) | 3.63352 | + | 6.29344i | 0.132501 | + | 0.229498i | ||||
\(753\) | 22.1885 | + | 38.4316i | 0.808594 | + | 1.40053i | ||||
\(754\) | 2.39688 | − | 4.15151i | 0.0872891 | − | 0.151189i | ||||
\(755\) | −18.8365 | −0.685532 | ||||||||
\(756\) | 35.3830 | + | 8.63797i | 1.28687 | + | 0.314160i | ||||
\(757\) | 17.8790 | 0.649822 | 0.324911 | − | 0.945745i | \(-0.394666\pi\) | ||||
0.324911 | + | 0.945745i | \(0.394666\pi\) | |||||||
\(758\) | −4.01245 | + | 6.94977i | −0.145739 | + | 0.252427i | ||||
\(759\) | −6.54951 | − | 11.3441i | −0.237732 | − | 0.411764i | ||||
\(760\) | 7.22799 | + | 12.5192i | 0.262187 | + | 0.454121i | ||||
\(761\) | 6.00551 | − | 10.4018i | 0.217699 | − | 0.377066i | −0.736405 | − | 0.676541i | \(-0.763478\pi\) |
0.954104 | + | 0.299475i | \(0.0968114\pi\) | |||||||
\(762\) | −22.3790 | −0.810707 | ||||||||
\(763\) | 32.7199 | + | 7.98784i | 1.18454 | + | 0.289179i | ||||
\(764\) | −4.93556 | −0.178562 | ||||||||
\(765\) | 83.3377 | − | 144.345i | 3.01308 | − | 5.21881i | ||||
\(766\) | −1.60796 | − | 2.78508i | −0.0580981 | − | 0.100629i | ||||
\(767\) | 0.358596 | + | 0.621107i | 0.0129482 | + | 0.0224269i | ||||
\(768\) | 1.60400 | − | 2.77821i | 0.0578793 | − | 0.100250i | ||||
\(769\) | 2.51353 | 0.0906402 | 0.0453201 | − | 0.998973i | \(-0.485569\pi\) | ||||
0.0453201 | + | 0.998973i | \(0.485569\pi\) | |||||||
\(770\) | 10.9025 | + | 37.3299i | 0.392899 | + | 1.34528i | ||||
\(771\) | −77.4704 | −2.79003 | ||||||||
\(772\) | 4.36238 | − | 7.55587i | 0.157006 | − | 0.271942i | ||||
\(773\) | −14.6047 | − | 25.2962i | −0.525296 | − | 0.909840i | −0.999566 | − | 0.0294602i | \(-0.990621\pi\) |
0.474270 | − | 0.880380i | \(-0.342712\pi\) | |||||||
\(774\) | −1.94067 | − | 3.36134i | −0.0697560 | − | 0.120821i | ||||
\(775\) | −6.09751 | + | 10.5612i | −0.219029 | + | 0.379370i | ||||
\(776\) | 16.4419 | 0.590231 | ||||||||
\(777\) | −6.20204 | + | 6.48572i | −0.222497 | + | 0.232674i | ||||
\(778\) | 3.58073 | 0.128375 | ||||||||
\(779\) | 5.05295 | − | 8.75197i | 0.181041 | − | 0.313572i | ||||
\(780\) | −5.38454 | − | 9.32629i | −0.192797 | − | 0.333935i | ||||
\(781\) | −11.9041 | − | 20.6185i | −0.425963 | − | 0.737789i | ||||
\(782\) | −3.17514 | + | 5.49951i | −0.113543 | + | 0.196662i | ||||
\(783\) | 70.7660 | 2.52897 | ||||||||
\(784\) | 6.21255 | + | 3.22555i | 0.221877 | + | 0.115198i | ||||
\(785\) | 70.8750 | 2.52964 | ||||||||
\(786\) | −13.5127 | + | 23.4047i | −0.481983 | + | 0.834819i | ||||
\(787\) | −10.7537 | − | 18.6260i | −0.383329 | − | 0.663945i | 0.608207 | − | 0.793778i | \(-0.291889\pi\) |
−0.991536 | + | 0.129833i | \(0.958556\pi\) | |||||||
\(788\) | 7.12066 | + | 12.3333i | 0.253663 | + | 0.439357i | ||||
\(789\) | 45.3999 | − | 78.6350i | 1.61628 | − | 2.79948i | ||||
\(790\) | 12.8393 | 0.456804 | ||||||||
\(791\) | −11.4717 | + | 11.9965i | −0.407888 | + | 0.426545i | ||||
\(792\) | −29.7719 | −1.05790 | ||||||||
\(793\) | −5.47083 | + | 9.47575i | −0.194275 | + | 0.336494i | ||||
\(794\) | 1.41750 | + | 2.45518i | 0.0503052 | + | 0.0871312i | ||||
\(795\) | −2.45055 | − | 4.24448i | −0.0869122 | − | 0.150536i | ||||
\(796\) | 6.86000 | − | 11.8819i | 0.243146 | − | 0.421141i | ||||
\(797\) | 16.0971 | 0.570190 | 0.285095 | − | 0.958499i | \(-0.407975\pi\) | ||||
0.285095 | + | 0.958499i | \(0.407975\pi\) | |||||||
\(798\) | −9.55537 | − | 32.7174i | −0.338256 | − | 1.15818i | ||||
\(799\) | −46.1478 | −1.63259 | ||||||||
\(800\) | −3.97924 | + | 6.89225i | −0.140688 | + | 0.243678i | ||||
\(801\) | 40.0387 | + | 69.3490i | 1.41470 | + | 2.45033i | ||||
\(802\) | 13.3428 | + | 23.1104i | 0.471151 | + | 0.816058i | ||||
\(803\) | −23.2692 | + | 40.3034i | −0.821152 | + | 1.42228i | ||||
\(804\) | 15.2666 | 0.538410 | ||||||||
\(805\) | 9.25242 | + | 2.25877i | 0.326105 | + | 0.0796113i | ||||
\(806\) | 1.42896 | 0.0503329 | ||||||||
\(807\) | −48.4854 | + | 83.9792i | −1.70677 | + | 2.95621i | ||||
\(808\) | −8.55232 | − | 14.8131i | −0.300870 | − | 0.521121i | ||||
\(809\) | −19.6424 | − | 34.0216i | −0.690590 | − | 1.19614i | −0.971645 | − | 0.236445i | \(-0.924018\pi\) |
0.281055 | − | 0.959692i | \(-0.409316\pi\) | |||||||
\(810\) | 40.1168 | − | 69.4844i | 1.40956 | − | 2.44143i | ||||
\(811\) | −35.6464 | −1.25172 | −0.625858 | − | 0.779937i | \(-0.715251\pi\) | ||||
−0.625858 | + | 0.779937i | \(0.715251\pi\) | |||||||
\(812\) | 13.2126 | + | 3.22555i | 0.463670 | + | 0.113195i | ||||
\(813\) | 29.3637 | 1.02983 | ||||||||
\(814\) | 2.15859 | − | 3.73879i | 0.0756587 | − | 0.131045i | ||||
\(815\) | 26.9498 | + | 46.6785i | 0.944011 | + | 1.63508i | ||||
\(816\) | 10.1858 | + | 17.6424i | 0.356576 | + | 0.617607i | ||||
\(817\) | −1.06886 | + | 1.85132i | −0.0373947 | + | 0.0647695i | ||||
\(818\) | 18.0247 | 0.630218 | ||||||||
\(819\) | 5.04327 | + | 17.2680i | 0.176226 | + | 0.603394i | ||||
\(820\) | 9.05904 | 0.316356 | ||||||||
\(821\) | −11.6972 | + | 20.2602i | −0.408236 | + | 0.707086i | −0.994692 | − | 0.102895i | \(-0.967189\pi\) |
0.586456 | + | 0.809981i | \(0.300523\pi\) | |||||||
\(822\) | 17.3107 | + | 29.9830i | 0.603780 | + | 1.04578i | ||||
\(823\) | 22.9229 | + | 39.7037i | 0.799044 | + | 1.38398i | 0.920240 | + | 0.391355i | \(0.127994\pi\) |
−0.121196 | + | 0.992629i | \(0.538673\pi\) | |||||||
\(824\) | 6.74962 | − | 11.6907i | 0.235134 | − | 0.407264i | ||||
\(825\) | 104.248 | 3.62946 | ||||||||
\(826\) | −1.40628 | + | 1.47061i | −0.0489309 | + | 0.0511690i | ||||
\(827\) | 40.7537 | 1.41715 | 0.708573 | − | 0.705638i | \(-0.249339\pi\) | ||||
0.708573 | + | 0.705638i | \(0.249339\pi\) | |||||||
\(828\) | −3.64562 | + | 6.31440i | −0.126694 | + | 0.219440i | ||||
\(829\) | −13.2097 | − | 22.8798i | −0.458791 | − | 0.794650i | 0.540106 | − | 0.841597i | \(-0.318384\pi\) |
−0.998897 | + | 0.0469470i | \(0.985051\pi\) | |||||||
\(830\) | −22.4172 | − | 38.8277i | −0.778111 | − | 1.34773i | ||||
\(831\) | 30.2425 | − | 52.3815i | 1.04910 | − | 1.81709i | ||||
\(832\) | 0.932540 | 0.0323300 | ||||||||
\(833\) | −37.4647 | + | 23.9244i | −1.29807 | + | 0.828931i | ||||
\(834\) | 25.2082 | 0.872889 | ||||||||
\(835\) | 9.14615 | − | 15.8416i | 0.316516 | − | 0.548221i | ||||
\(836\) | 8.19870 | + | 14.2006i | 0.283558 | + | 0.491137i | ||||
\(837\) | 10.5472 | + | 18.2683i | 0.364566 | + | 0.631447i | ||||
\(838\) | −0.352347 | + | 0.610282i | −0.0121716 | + | 0.0210819i | ||||
\(839\) | 9.35546 | 0.322986 | 0.161493 | − | 0.986874i | \(-0.448369\pi\) | ||||
0.161493 | + | 0.986874i | \(0.448369\pi\) | |||||||
\(840\) | 21.1162 | − | 22.0821i | 0.728578 | − | 0.761904i | ||||
\(841\) | −2.57489 | −0.0887894 | ||||||||
\(842\) | −5.12041 | + | 8.86882i | −0.176461 | + | 0.305640i | ||||
\(843\) | 19.4366 | + | 33.6652i | 0.669433 | + | 1.15949i | ||||
\(844\) | −0.982052 | − | 1.70096i | −0.0338036 | − | 0.0585496i | ||||
\(845\) | −21.8334 | + | 37.8165i | −0.751091 | + | 1.30093i | ||||
\(846\) | −52.9857 | −1.82169 | ||||||||
\(847\) | 4.20771 | + | 14.4071i | 0.144579 | + | 0.495034i | ||||
\(848\) | 0.424408 | 0.0145742 | ||||||||
\(849\) | −21.1876 | + | 36.6981i | −0.727158 | + | 1.25947i | ||||
\(850\) | −25.2693 | − | 43.7678i | −0.866731 | − | 1.50122i | ||||
\(851\) | −0.528647 | − | 0.915643i | −0.0181218 | − | 0.0313878i | ||||
\(852\) | −9.35246 | + | 16.1989i | −0.320410 | + | 0.554966i | ||||
\(853\) | −31.8348 | −1.09000 | −0.545001 | − | 0.838435i | \(-0.683471\pi\) | ||||
−0.545001 | + | 0.838435i | \(0.683471\pi\) | |||||||
\(854\) | −30.1574 | − | 7.36226i | −1.03197 | − | 0.251931i | ||||
\(855\) | −105.402 | −3.60467 | ||||||||
\(856\) | −3.51297 | + | 6.08465i | −0.120071 | + | 0.207969i | ||||
\(857\) | 10.7230 | + | 18.5728i | 0.366292 | + | 0.634436i | 0.988983 | − | 0.148032i | \(-0.0472938\pi\) |
−0.622691 | + | 0.782468i | \(0.713961\pi\) | |||||||
\(858\) | −6.10768 | − | 10.5788i | −0.208513 | − | 0.361155i | ||||
\(859\) | −13.3164 | + | 23.0647i | −0.454350 | + | 0.786958i | −0.998651 | − | 0.0519325i | \(-0.983462\pi\) |
0.544300 | + | 0.838891i | \(0.316795\pi\) | |||||||
\(860\) | −1.91628 | −0.0653445 | ||||||||
\(861\) | −20.7500 | − | 5.06564i | −0.707157 | − | 0.172637i | ||||
\(862\) | −32.9490 | −1.12225 | ||||||||
\(863\) | −20.2714 | + | 35.1110i | −0.690045 | + | 1.19519i | 0.281777 | + | 0.959480i | \(0.409076\pi\) |
−0.971823 | + | 0.235714i | \(0.924257\pi\) | |||||||
\(864\) | 6.88314 | + | 11.9219i | 0.234169 | + | 0.405593i | ||||
\(865\) | −21.6436 | − | 37.4877i | −0.735903 | − | 1.27462i | ||||
\(866\) | −12.3617 | + | 21.4112i | −0.420069 | + | 0.727581i | ||||
\(867\) | −74.8300 | −2.54136 | ||||||||
\(868\) | 1.13657 | + | 3.89159i | 0.0385777 | + | 0.132089i | ||||
\(869\) | 14.5637 | 0.494039 | ||||||||
\(870\) | 29.6817 | − | 51.4103i | 1.00631 | − | 1.74297i | ||||
\(871\) | 2.21894 | + | 3.84331i | 0.0751858 | + | 0.130226i | ||||
\(872\) | 6.36508 | + | 11.0246i | 0.215549 | + | 0.373341i | ||||
\(873\) | −59.9410 | + | 103.821i | −2.02870 | + | 3.51381i | ||||
\(874\) | 4.01578 | 0.135836 | ||||||||
\(875\) | −19.4739 | + | 20.3646i | −0.658336 | + | 0.688449i | ||||
\(876\) | 36.5628 | 1.23534 | ||||||||
\(877\) | 11.0378 | − | 19.1180i | 0.372719 | − | 0.645568i | −0.617264 | − | 0.786756i | \(-0.711759\pi\) |
0.989983 | + | 0.141188i | \(0.0450923\pi\) | |||||||
\(878\) | 7.30561 | + | 12.6537i | 0.246552 | + | 0.427041i | ||||
\(879\) | 23.8554 | + | 41.3187i | 0.804622 | + | 1.39365i | ||||
\(880\) | −7.34941 | + | 12.7295i | −0.247748 | + | 0.429113i | ||||
\(881\) | −55.1259 | −1.85724 | −0.928619 | − | 0.371034i | \(-0.879003\pi\) | ||||
−0.928619 | + | 0.371034i | \(0.879003\pi\) | |||||||
\(882\) | −43.0160 | + | 27.4694i | −1.44842 | + | 0.924943i | ||||
\(883\) | −1.32125 | −0.0444638 | −0.0222319 | − | 0.999753i | \(-0.507077\pi\) | ||||
−0.0222319 | + | 0.999753i | \(0.507077\pi\) | |||||||
\(884\) | −2.96095 | + | 5.12851i | −0.0995874 | + | 0.172490i | ||||
\(885\) | 4.44068 | + | 7.69148i | 0.149272 | + | 0.258546i | ||||
\(886\) | 10.6276 | + | 18.4075i | 0.357040 | + | 0.618411i | ||||
\(887\) | 11.3116 | − | 19.5923i | 0.379806 | − | 0.657844i | −0.611227 | − | 0.791455i | \(-0.709324\pi\) |
0.991034 | + | 0.133611i | \(0.0426573\pi\) | |||||||
\(888\) | −3.39179 | −0.113821 | ||||||||
\(889\) | 12.7559 | − | 13.3394i | 0.427821 | − | 0.447389i | ||||
\(890\) | 39.5354 | 1.32523 | ||||||||
\(891\) | 45.5045 | − | 78.8162i | 1.52446 | − | 2.64044i | ||||
\(892\) | −3.50333 | − | 6.06795i | −0.117300 | − | 0.203170i | ||||
\(893\) | 14.5914 | + | 25.2731i | 0.488283 | + | 0.845732i | ||||
\(894\) | −16.7905 | + | 29.0820i | −0.561557 | + | 0.972646i | ||||
\(895\) | 28.7617 | 0.961398 | ||||||||
\(896\) | 0.741726 | + | 2.53965i | 0.0247793 | + | 0.0848439i | ||||
\(897\) | −2.99158 | −0.0998861 | ||||||||
\(898\) | 15.0280 | − | 26.0292i | 0.501491 | − | 0.868607i | ||||
\(899\) | 3.93850 | + | 6.82168i | 0.131356 | + | 0.227516i | ||||
\(900\) | −29.0136 | − | 50.2531i | −0.967121 | − | 1.67510i | ||||
\(901\) | −1.34755 | + | 2.33403i | −0.0448936 | + | 0.0777579i | ||||
\(902\) | 10.2757 | 0.342143 | ||||||||
\(903\) | 4.38928 | + | 1.07154i | 0.146066 | + | 0.0356588i | ||||
\(904\) | −6.27371 | −0.208660 | ||||||||
\(905\) | 0.945748 | − | 1.63808i | 0.0314377 | − | 0.0544517i | ||||
\(906\) | 8.39320 | + | 14.5375i | 0.278845 | + | 0.482974i | ||||
\(907\) | −5.84787 | − | 10.1288i | −0.194175 | − | 0.336321i | 0.752455 | − | 0.658644i | \(-0.228870\pi\) |
−0.946630 | + | 0.322323i | \(0.895536\pi\) | |||||||
\(908\) | 12.5699 | − | 21.7716i | 0.417145 | − | 0.722517i | ||||
\(909\) | 124.714 | 4.13650 | ||||||||
\(910\) | 8.62825 | + | 2.10640i | 0.286024 | + | 0.0698263i | ||||
\(911\) | −24.2629 | −0.803867 | −0.401933 | − | 0.915669i | \(-0.631662\pi\) | ||||
−0.401933 | + | 0.915669i | \(0.631662\pi\) | |||||||
\(912\) | 6.44131 | − | 11.1567i | 0.213293 | − | 0.369434i | ||||
\(913\) | −25.4278 | − | 44.0422i | −0.841537 | − | 1.45758i | ||||
\(914\) | −1.48247 | − | 2.56771i | −0.0490357 | − | 0.0849323i | ||||
\(915\) | −67.7480 | + | 117.343i | −2.23968 | + | 3.87924i | ||||
\(916\) | −15.8424 | −0.523447 | ||||||||
\(917\) | −6.24860 | − | 21.3951i | −0.206347 | − | 0.706528i | ||||
\(918\) | −87.4197 | −2.88528 | ||||||||
\(919\) | 10.6854 | − | 18.5077i | 0.352479 | − | 0.610512i | −0.634204 | − | 0.773166i | \(-0.718672\pi\) |
0.986683 | + | 0.162654i | \(0.0520053\pi\) | |||||||
\(920\) | 1.79990 | + | 3.11751i | 0.0593408 | + | 0.102781i | ||||
\(921\) | −17.1102 | − | 29.6358i | −0.563802 | − | 0.976533i | ||||
\(922\) | 8.08043 | − | 13.9957i | 0.266115 | − | 0.460925i | ||||
\(923\) | −5.43737 | −0.178973 | ||||||||
\(924\) | 23.9521 | − | 25.0477i | 0.787967 | − | 0.824009i | ||||
\(925\) | 8.41446 | 0.276666 | ||||||||
\(926\) | 16.0915 | − | 27.8713i | 0.528799 | − | 0.915907i | ||||
\(927\) | 49.2131 | + | 85.2395i | 1.61637 | + | 2.79963i | ||||
\(928\) | 2.57027 | + | 4.45183i | 0.0843732 | + | 0.146139i | ||||
\(929\) | −3.27342 | + | 5.66973i | −0.107397 | + | 0.186018i | −0.914715 | − | 0.404099i | \(-0.867585\pi\) |
0.807318 | + | 0.590117i | \(0.200918\pi\) | |||||||
\(930\) | 17.6955 | 0.580259 | ||||||||
\(931\) | 24.9483 | + | 12.9531i | 0.817646 | + | 0.424521i | ||||
\(932\) | 5.12497 | 0.167874 | ||||||||
\(933\) | −27.1271 | + | 46.9856i | −0.888103 | + | 1.53824i | ||||
\(934\) | 1.84930 | + | 3.20308i | 0.0605109 | + | 0.104808i | ||||
\(935\) | −46.6708 | − | 80.8362i | −1.52630 | − | 2.64363i | ||||
\(936\) | −3.39969 | + | 5.88843i | −0.111122 | + | 0.192469i | ||||
\(937\) | 42.1077 | 1.37560 | 0.687799 | − | 0.725902i | \(-0.258577\pi\) | ||||
0.687799 | + | 0.725902i | \(0.258577\pi\) | |||||||
\(938\) | −8.70186 | + | 9.09989i | −0.284126 | + | 0.297122i | ||||
\(939\) | −84.8126 | −2.76775 | ||||||||
\(940\) | −13.0799 | + | 22.6551i | −0.426620 | + | 0.738927i | ||||
\(941\) | 6.43587 | + | 11.1473i | 0.209803 | + | 0.363390i | 0.951653 | − | 0.307177i | \(-0.0993843\pi\) |
−0.741849 | + | 0.670567i | \(0.766051\pi\) | |||||||
\(942\) | −31.5806 | − | 54.6991i | −1.02895 | − | 1.78219i | ||||
\(943\) | 1.25827 | − | 2.17939i | 0.0409750 | − | 0.0709708i | ||||
\(944\) | −0.769075 | −0.0250312 | ||||||||
\(945\) | 36.7567 | + | 125.854i | 1.19570 | + | 4.09404i | ||||
\(946\) | −2.17363 | −0.0706709 | ||||||||
\(947\) | 12.1418 | − | 21.0302i | 0.394556 | − | 0.683390i | −0.598489 | − | 0.801131i | \(-0.704232\pi\) |
0.993044 | + | 0.117741i | \(0.0375652\pi\) | |||||||
\(948\) | −5.72097 | − | 9.90901i | −0.185808 | − | 0.321830i | ||||
\(949\) | 5.31427 | + | 9.20458i | 0.172508 | + | 0.298793i | ||||
\(950\) | −15.9798 | + | 27.6778i | −0.518452 | + | 0.897986i | ||||
\(951\) | −68.1911 | −2.21125 | ||||||||
\(952\) | −16.3219 | − | 3.98463i | −0.528997 | − | 0.129143i | ||||
\(953\) | 6.91655 | 0.224049 | 0.112025 | − | 0.993705i | \(-0.464266\pi\) | ||||
0.112025 | + | 0.993705i | \(0.464266\pi\) | |||||||
\(954\) | −1.54723 | + | 2.67988i | −0.0500934 | + | 0.0867643i | ||||
\(955\) | −8.88349 | − | 15.3867i | −0.287463 | − | 0.497900i | ||||
\(956\) | 6.60347 | + | 11.4376i | 0.213572 | + | 0.369917i | ||||
\(957\) | 33.6680 | − | 58.3147i | 1.08833 | − | 1.88505i | ||||
\(958\) | −37.5565 | −1.21340 | ||||||||
\(959\) | −27.7389 | − | 6.77183i | −0.895736 | − | 0.218674i | ||||
\(960\) | 11.5481 | 0.372714 | ||||||||
\(961\) | 14.3260 | − | 24.8133i | 0.462128 | − | 0.800430i | ||||
\(962\) | −0.492984 | − | 0.853874i | −0.0158945 | − | 0.0275300i | ||||
\(963\) | −25.6139 | − | 44.3646i | −0.825397 | − | 1.42963i | ||||
\(964\) | −13.8311 | + | 23.9562i | −0.445470 | + | 0.771577i | ||||
\(965\) | 31.4073 | 1.01104 | ||||||||
\(966\) | −2.37945 | − | 8.14720i | −0.0765577 | − | 0.262132i | ||||
\(967\) | 18.2218 | 0.585972 | 0.292986 | − | 0.956117i | \(-0.405351\pi\) | ||||
0.292986 | + | 0.956117i | \(0.405351\pi\) | |||||||
\(968\) | −2.83643 | + | 4.91285i | −0.0911664 | + | 0.157905i | ||||
\(969\) | 40.9041 | + | 70.8480i | 1.31403 | + | 2.27597i | ||||
\(970\) | 29.5938 | + | 51.2579i | 0.950199 | + | 1.64579i | ||||
\(971\) | 24.2880 | − | 42.0681i | 0.779439 | − | 1.35003i | −0.152826 | − | 0.988253i | \(-0.548837\pi\) |
0.932265 | − | 0.361776i | \(-0.117829\pi\) | |||||||
\(972\) | −30.2024 | −0.968742 | ||||||||
\(973\) | −14.3686 | + | 15.0258i | −0.460635 | + | 0.481705i | ||||
\(974\) | −17.7566 | −0.568958 | ||||||||
\(975\) | 11.9042 | − | 20.6188i | 0.381241 | − | 0.660329i | ||||
\(976\) | −5.86659 | − | 10.1612i | −0.187785 | − | 0.325253i | ||||
\(977\) | 13.8576 | + | 24.0022i | 0.443345 | + | 0.767897i | 0.997935 | − | 0.0642270i | \(-0.0204582\pi\) |
−0.554590 | + | 0.832124i | \(0.687125\pi\) | |||||||
\(978\) | 24.0167 | − | 41.5981i | 0.767968 | − | 1.33016i | ||||
\(979\) | 44.8450 | 1.43325 | ||||||||
\(980\) | 1.12626 | + | 25.1733i | 0.0359772 | + | 0.804133i | ||||
\(981\) | −92.8186 | −2.96347 | ||||||||
\(982\) | −3.46897 | + | 6.00843i | −0.110699 | + | 0.191737i | ||||
\(983\) | 7.51872 | + | 13.0228i | 0.239810 | + | 0.415363i | 0.960660 | − | 0.277728i | \(-0.0895815\pi\) |
−0.720850 | + | 0.693091i | \(0.756248\pi\) | |||||||
\(984\) | −4.03654 | − | 6.99149i | −0.128680 | − | 0.222881i | ||||
\(985\) | −25.6329 | + | 44.3974i | −0.816731 | + | 1.41462i | ||||
\(986\) | −32.6439 | −1.03959 | ||||||||
\(987\) | 42.6281 | − | 44.5780i | 1.35687 | − | 1.41893i | ||||
\(988\) | 3.74488 | 0.119140 | ||||||||
\(989\) | −0.266165 | + | 0.461011i | −0.00846355 | + | 0.0146593i | ||||
\(990\) | −53.5863 | − | 92.8142i | −1.70308 | − | 2.94983i | ||||
\(991\) | −23.4463 | − | 40.6101i | −0.744795 | − | 1.29002i | −0.950291 | − | 0.311365i | \(-0.899214\pi\) |
0.205496 | − | 0.978658i | \(-0.434119\pi\) | |||||||
\(992\) | −0.766165 | + | 1.32704i | −0.0243258 | + | 0.0421335i | ||||
\(993\) | 77.4567 | 2.45801 | ||||||||
\(994\) | −4.32479 | − | 14.8080i | −0.137174 | − | 0.469681i | ||||
\(995\) | 49.3891 | 1.56574 | ||||||||
\(996\) | −19.9773 | + | 34.6017i | −0.633006 | + | 1.09640i | ||||
\(997\) | −10.5901 | − | 18.3426i | −0.335391 | − | 0.580915i | 0.648169 | − | 0.761497i | \(-0.275535\pi\) |
−0.983560 | + | 0.180582i | \(0.942202\pi\) | |||||||
\(998\) | 2.79593 | + | 4.84269i | 0.0885036 | + | 0.153293i | ||||
\(999\) | 7.27750 | − | 12.6050i | 0.230250 | − | 0.398804i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 322.2.e.b.93.4 | ✓ | 8 | |
7.2 | even | 3 | 2254.2.a.w.1.1 | 4 | |||
7.4 | even | 3 | inner | 322.2.e.b.277.4 | yes | 8 | |
7.5 | odd | 6 | 2254.2.a.ba.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.2.e.b.93.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
322.2.e.b.277.4 | yes | 8 | 7.4 | even | 3 | inner | |
2254.2.a.w.1.1 | 4 | 7.2 | even | 3 | |||
2254.2.a.ba.1.4 | 4 | 7.5 | odd | 6 |